WASHINGTON — President Trump announced on Tuesday that he had fired John R. Bolton, his third national security adviser, on Tuesday amid fundamental disagreements over how to handle major foreign policy challenges like Iran, North Korea and most recently Afghanistan.

“I informed John Bolton last night that his services are no longer needed at the White House,” the president wrote on Twitter. “I disagreed strongly with many of his suggestions, as did others in the Administration, and therefore I asked John for his resignation, which was given to me this morning. I thank John very much for his service.”

Mr. Bolton offered a different version of how the end came in his own message on Twitter shortly afterward. “I offered to resign last night and President Trump said, ‘Let’s talk about it tomorrow,’” Mr. Bolton wrote, without elaborating.

Responding to a question from The New York Times via text message, Mr. Bolton said it was his initiative. “Offered last night without his asking,” he wrote. “Slept on it and gave it to him this morning.”

Mr. Trump named no successor but said he would appoint someone “next week,” setting off a process that should reveal where the president wants to take his foreign policy in the remaining time before next year’s election.

The national security adviser’s dismissal came so abruptly that it was announced barely an hour after the White House scheduled a briefing for 2:30 p.m. where Mr. Bolton was supposed to appear alongside Secretary of State Mike Pompeo and Treasury Secretary Steven Mnuchin. But Mr. Bolton is reported to have now left the White House.

Mr. Bolton’s departure comes as Mr. Trump is pursuing diplomatic openings with some of the United States’ most intractable enemies, efforts that have troubled hard-liners in the administration, like Mr. Bolton, who view North Korea and Iran as profoundly untrustworthy.

He spent much of the last week waging a last-minute battle to prevent Mr. Trump from signing off on a peace agreement with the Taliban militant organization, which he viewed as anathema — a deal that the president was preparing to finalize by inviting the Taliban leaders to Camp David.

Mr. Bolton urged Mr. Trump to reject the agreement, arguing that the president could still withdraw troops from Afghanistan to fulfill his campaign promise without getting in bed with an organization responsible for killing thousands of Americans over the last 18 years.

Mr. Trump ultimately did scrap plans for the Camp David meeting and said on Monday that talks with the Taliban were now “dead.” But he was irritated by Mr. Bolton, who was feuding with Mr. Pompeo for months.

Mr. Bolton saw his job as stopping Mr. Trump from making unwise agreements with America’s enemies.” While John Bolton was national security adviser for the last 17 months, there have been no bad deals,” a person close to Mr. Bolton said minutes after the president’s announcement on Tuesday, reflecting the ousted adviser’s view.

To Mr. Bolton’s aggravation, the president has continued to court Kim Jong-un, the repressive leader of North Korea, despite Mr. Kim’s refusal to surrender his nuclear program and despite repeated short-range missile tests by the North that have rattled its neighbors. In recent days, Mr. Trump has expressed a willingness to meet with President Hassan Rouhani of Iran under the right circumstances, and even to extend short-term financing to Tehran, although the offer has so far been rebuffed.

The rift between the president and his national security adviser owed as much to personality as to policy. The president never warmed to him, a dynamic that is often fatal in this White House.

At its core, the schism reflected a deep-seated philosophical difference that has characterized the Trump presidency. While given to bellicose language, Mr. Trump came to office deeply skeptical of overseas military adventures and promising negotiations to resolve volatile conflicts. Mr. Bolton, however, has been one of Washington’s most outspoken hawks and unapologetic advocates of American power to defend the country’s interests.

To his admirers, Mr. Bolton was supposed to be a check on what they feared would be naïve diplomacy, a cleareyed realist who would keep a president without prior experience in foreign affairs from giving away the store to wily adversaries. But Mr. Trump has long complained privately that Mr. Bolton was too willing to get the United States into another war.

The tension between the men was aggravated in recent months by the president’s decisions to call off a planned airstrike on Iran in retaliation for the downing of an American surveillance drone and to meet with Mr. Kim at the Demilitarized Zone and cross over into North Korea.

Mr. Bolton favored the strike on Iran and publicly criticized recent North Korean missile tests that Mr. Trump brushed off. After the president arranged the DMZ meeting with Mr. Kim via a last-minute Twitter message, Mr. Bolton opted not to accompany him and instead proceeded on a previously scheduled trip to Mongolia.

A former under secretary of state and ambassador to the United Nations under President George W. Bush, Mr. Bolton, 70, never fully subscribed to Mr. Trump’s courtship of Mr. Kim and privately expressed frustration that the president was unwilling to take more meaningful action to transform the Middle East in the service of American interests.

Mr. Bolton was hamstrung in his ability to steer Mr. Trump in what he saw as the right direction. He also clashed with officials at the Defense Department. At one point, military officials expressed alarm at Mr. Bolton’s requests for contingency war plans.

While in office, Mr. Bolton sought to minimize his differences with the president in public. After Mr. Trump said he would be open to meeting with Mr. Rouhani and even to extending a line of credit to help Tehran get through its financial difficulties while talks proceeded, Mr. Bolton insisted that did not reflect a concession by the president.

“He’ll meet with anybody to talk,” Mr. Bolton told Radio Free Europe/Radio Liberty. “He is a negotiator. He is a deal maker. But talking with them does not imply — for President Trump, does not imply changing your position.”

Appointed in spring 2018, Mr. Bolton followed Michael T. Flynn — who stepped down as national security adviser after 24 days and later pleaded guilty to lying to the F.B.I. — and his successor, Lt. Gen. H.R. McMaster, who never forged a strong connection with the president and was forced out.

In choosing Mr. Bolton, Mr. Trump appreciated his outspoken performances on Fox News and wanted a contrast to the current and retired generals who were perceived as running his foreign policy team. Mr. Bolton also had the strong backing of Sheldon G. Adelson, the casino magnate and Republican megadonor who is a key supporter of Mr. Trump.

Long before Mr. Trump popularized his “America First” slogan, Mr. Bolton termed himself an “Americanist” who prioritized a cold-eyed view of national interests and sovereignty over what they both saw as a fuzzy-headed fixation on democracy promotion and human rights. They shared a deep skepticism of globalism and multilateralism, a commonality that empowered Mr. Bolton to use his time in the White House to orchestrate the withdrawal of the United States from arms control treaties and other international agreements.

With Mr. Trump’s backing, Mr. Bolton likewise helped enact policies meant to pressure the Communist government in Cuba, reversing some but not all of the measures taken by President Barack Obama in a diplomatic opening to the island. Among other things, the Trump administration imposed limits on travel and remittances to Cuba and opened the door to lawsuits by Americans whose property was seized in the revolution in 1959.

But if Mr. Trump’s original national security team was seen as restraining a mercurial new commander in chief, the president found himself sometimes restraining Mr. Bolton. Behind the scenes, he joked about Mr. Bolton’s penchant for confrontation. “If it was up to John, we’d be in four wars now,” one senior official recalled the president saying.

Mr. Trump also grew disenchanted with Mr. Bolton over the failed effort to push out President Nicolás Maduro of Venezuela. Rather than the easy victory he was led to anticipate, the president has found himself bogged down in a conflict over which he has less influence than he had assumed. The political opposition backed by the White House could not turn Venezuela’s military against Mr. Maduro and has been stuck in a stalemate for months.

The divergence between the two men was on display in May during the president’s first trip this year to Japan. After Mr. Bolton told reporters then that “there is no doubt” that North Korean short-range missile launches violated United Nations resolutions, Mr. Trump dismissed the concern, still eager to preserve his strained relationship with Mr. Kim.

“My people think it could have been a violation, as you know,” the president told reporters. “I view it differently.”

Mr. Trump likewise repudiated an idea of working to overthrow the government of Iran, a goal Mr. Bolton long advanced as a private citizen. “We’re not looking for regime change,” Mr. Trump said. “I just want to make that clear.”

After Iran was accused in June of damaging two tankers with explosives and then shot down the drone, Mr. Bolton favored a demonstration of force. He facilitated a recommendation by the national security team for an airstrike against Iranian radar and other facilities, which Mr. Trump initially accepted only to change his mind at the last minute out of what he said was concern over casualties that would result.

Mr. Bolton’s later absence from Mr. Trump’s trip to the DMZ and hourlong meeting with Mr. Kim seemed conspicuous. Mr. Bolton’s staff said he was only following through on his schedule by going to Mongolia, but right or wrong, it was taken as a sign that he was not fully on board with the president’s diplomatic overture to North Korea.

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