WASHINGTON — President Trump’s abrupt ouster of John Bolton, his hawkish national security adviser, has reignited concerns among some Republicans in Congress about the White House’s waning interest in projecting American military power around the world, a doctrine that was once the subject of a powerful consensus in their party.

It is the latest sign of the divide among Republican lawmakers on national security, pitting a camp of hawkish conservatives including Representative Liz Cheney, the House’s third-ranking Republican, and Senator Mitt Romney, the 2012 GOP presidential nominee, against a newer, anti-establishment group aligned with Mr. Trump’s impulses to put an end to the nation’s intractable military conflicts.

Mr. Bolton’s exit, announced by Mr. Trump on Twitter on Tuesday, following Mr. Trump’s revelation that he had scheduled — and then scrapped — plans to meet with the Taliban for peace talks at Camp David, dramatized the rift.

Senator Mitch McConnell of Kentucky, the majority leader, praised Mr. Bolton’s leadership on Wednesday in comments that appeared to be directed at the White House.

“He knows there are many threats to American interests and that those threats will not recede if we retreat,” Mr. McConnell said from the Senate floor. “He understands that American leadership is essential to keeping these threats and enemies at bay, and that our partners and allies rarely act without us.”

Mr. Romney called Mr. Bolton’s departure “an extraordinary loss for our nation and the White House,” expressing deep concern about how Mr. Trump would move forward in Afghanistan following his departure.

CreditTom Brenner for The New York Times

“We have to regroup and decide how we’re going to proceed, but it’s certainly essential that Afghanistan not be allowed to return as a base for terrorist activity,” said Mr. Romney, a frequent critic of Mr. Trump who sits on the Foreign Relations Committee. “And that will mean an ongoing American presence there unless we see a very different response from the Taliban.”

Ms. Cheney, an ally of the president, had expressed alarm about Mr. Trump’s apparent willingness to host the Taliban at the presidential retreat.

“Camp David is where America’s leaders met to plan our response after Al Qaeda, supported by the Taliban, killed 3,000 Americans,” Ms. Cheney, wrote on Twitter. “No member of the Taliban should set foot there. Ever. The Taliban still harbors Al Qaeda. The President is right to end the talks.”

But in the Senate, Rand Paul of Kentucky, a libertarian-minded Republican who has made disengaging from foreign military conflict a calling card, hastily scheduled a conference call with reporters to congratulate Mr. Trump for jettisoning Mr. Bolton.

During a separate interview, on the heels of the president’s decision to abandon negotiations with the Taliban, Mr. Paul again made the case for a withdrawal of United States troops from Afghanistan.

“I think they will fight until the end of time,” Mr. Paul said, noting that he has several family members and friends in the military. “I have a tough time sending them to potentially lose their lives in Afghanistan when I can’t delineate what their mission is, the reason we’re there any more.”

Mr. Trump’s allies argued that Mr. Bolton’s departure signaled that Mr. Trump was reasserting his own stamp on foreign policy.

CreditErin Schaff/The New York Times

“The president is very hawkish when it comes to dealing with the economic realm, but when it comes to war fighting, he’s got that more populist, even libertarian strain to him,” said Senator Kevin Cramer, Republican of North Dakota, who is an ally of the president and sits on the Armed Services Committee. “The Bolton dismissal is an outcome of that push and pull,” Mr. Cramer continued, adding that Mr. Bolton “pushed maybe too hard.”

It is not the first time the president’s foreign policy has left Republican lawmakers crosswise with the White House, provoking their dissent in a way that perhaps no other issue has. In June, when Mr. Trump abruptly reversed his decision to launch a military strike against Iran after an American spy plane was shot down, national security hawks in his party, including Ms. Cheney, publicly lamented the decision. Mr. McConnell led Senate Republicans in January — as well as a group of Democrats — in delivering a pointed rebuke of the president’s announced withdrawal of United States military forces from Syria and Afghanistan.

Those who have frequently found themselves in lock step with Mr. Bolton, a cadre of hawkish lawmakers, many of whom have defense and military backgrounds, are now without a key ally in the White House. But they walked away early this week with a victory, praising Mr. Trump’s decision to cancel the negotiations to end the war with the Taliban. Those lawmakers have argued that Mr. Trump must not withdraw U.S. forces from Afghanistan based on a political timetable, and that any deal with the Taliban should be viewed with the utmost skepticism.

“We can’t just wish the war away because it’s been long, hard and difficult,” said Representative Michael Waltz, Republican of Florida, who is a former Army Special Forces officer who served in Afghanistan. “Just because it’s difficult doesn’t mean it’s not worth doing. And in my view, we need to stay on offense, we need to keep our foot on their neck, we need them worrying about where they can sleep at night.”

The president’s frequent changes of heart on national security issues have also taught Republicans to hope that on crucial decisions, he will oscillate toward their preferred approach. He routinely voices frustration with the worldview that suggests the United States bears responsibility for patrolling the globe, and on Monday groused that soldiers in Afghanistan were serving, to a large extent, as policemen. Those comments have stoked hope among noninterventionists like Mr. Paul that the president will follow his instincts and make good on his campaign pledge.

“I’ve talked to him dozens of times, and I do believe the president wants to end the war in Afghanistan,” Mr. Paul said. “But he’s surrounded by people telling him all kinds of reasons why he can’t.”

Intent on ensuring Mr. Trump delivers on his campaign promise to end the forever wars, organizations like FreedomWorks, a libertarian advocacy group associated with the Tea Party, and Concerned Veterans for America, one of the arms of the Koch network, have mounted lobbying campaigns on Capitol Hill in an effort to provide political cover for Republicans who back ending military engagement in Afghanistan. They have found support from strident conservatives in the House, like Representative Matt Gaetz of Florida and Representative Andy Biggs of Arizona.

“At the end of the day, we didn’t end up in an endless war in Syria or Iran, and I think that is more reflective of the president’s view than his staff’s,” said Mr. Gaetz, a close ally of Mr. Trump. “I think the president has been pretty consistent in his desire to not start a new forever war, and I think the country can even be more heartened in that ideology with Mr. Bolton’s departure.”

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