Mark Sanford, the former governor and representative from South Carolina who lost re-election to Congress after becoming a vocal critic of President Trump, announced on Sunday that he would seek the Republican presidential nomination and challenge the man who helped doom his 2018 primary campaign.

“I am going to get in,” Mr. Sanford said in an interview broadcast on “Fox News Sunday.”

“I think we need to have a conversation on what it means to be a Republican,” he added. “I think that as a Republican Party we have lost our way.”

Mr. Sanford had been mulling a presidential primary run since at least mid-July when he told The Post and Courier of Charleston, S.C., that he was considering whether and how he could focus national attention on the need to rein in government spending.

With his announcement on Sunday, Mr. Sanford, 59, joins the Tea Party Republican and one-term congressman Joe Walsh of Illinois and William F. Weld, the former Massachusetts governor, as Mr. Trump’s primary opponents. Mr. Walsh is seeking to challenge Mr. Trump from the right as Mr. Weld has quietly campaigned from closer to the center. And, now, Mr. Sanford will take on the president from his perch as a budget hawk.

The federal deficit has ballooned during the Trump presidency and will widen to $1 trillion for the 2020 fiscal year, the Congressional Budget Office said in forecasts released in August.

[Who’s running for president? Our list of who’s in and who’s out.]

Approval ratings among Republicans for Mr. Trump are consistently in the high 80s. He is virtually guaranteed to win the Republican presidential nomination. But some conservative opponents of Mr. Trump have suggested that the three candidates in combination could hobble him, or at least get under his skin.

For his part, Mr. Trump last month boasted about his approval rating among Republicans and attacked Mr. Sanford, Mr. Walsh and Mr. Weld. In Mr. Sanford’s case, the president, who himself has been accused of infidelity, made an allusion to the former congressman’s extramarital affair in 2009.

Mr. Sanford supported Mr. Trump in 2016 but eventually became one of his most vocal Republican critics in Congress. Last summer, he lost the primary to Katie Arrington, a candidate Mr. Trump had endorsed. Ms. Arrington would go on to lose in the general election to her Democratic opponent, Joe Cunningham.

“Republicans got a wake-up call last week. But will we wake up?” Mr. Sanford wrote in an Op-Ed in The New York Times shortly after Ms. Arrington was defeated. “My party would be wise to take a step back from President Trump’s approach to politics.”

In two stints in the House of Representatives, where he served a total of six terms, Mr. Sanford was regarded as one of the body’s most fiscally conservative members. As governor he went so far as to try to reject $700 million in federal funds sent to his state following the recession.

His second term as South Carolina governor was marred by the disclosure of the extramarital affair, which he acknowledged following an unexplained and highly publicized disappearance that lasted nearly a week. He had claimed to be hiking the Appalachian Trail, but he instead was in Argentina with his girlfriend.

Despite the scandal, Mr. Sanford was re-elected in 2013 to the congressional seat he had held before becoming governor.

Annoyed by the criticism from Mr. Sanford, Mr. Trump unleashed a Twitter attack hours before the polls closed on the day of Mr. Sanford’s primary.

“Mark Sanford has been very unhelpful to me in my campaign to MAGA,” Mr. Trump wrote. “He is MIA and nothing but trouble. He is better off in Argentina.”

The tweet helped seal Mr. Sanford’s defeat.

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