Mike Pence, Donald J. Trump’s former vice president, indicated on Friday that he would not be falling into line behind the presumptive Republican presidential nominee, as some of Mr. Trump’s other previous rivals including Ron DeSantis, Vivek Ramaswamy and Tim Scott did.

When asked whether he would endorse Mr. Trump now that the former president had clinched the party’s nomination, Mr. Pence told Fox News that he “could not in good conscience” support him.

“It should come as no surprise that I will not be endorsing Donald Trump this year,” he said.

The former vice president declined to say whether he would vote for Mr. Trump in the November election, but answered, “I would never vote for Joe Biden.” He also ruled out running as a third-party or independent candidate for president, saying he remained a Republican.

The Trump campaign did not immediately respond to a request for comment on Friday.

In his less than five months as a candidate for the Republican presidential nomination, Mr. Pence struggled to gain traction with caucusgoers and primary voters who remained very loyal to Mr. Trump.

He repeatedly rebuked Mr. Trump, his onetime running mate, for his actions during the Jan. 6, 2021, attack on the U.S. Capitol while at the same time seeking to take credit for the Trump-Pence administration’s record in areas that included the economy and judicial appointments.

Mr. Pence incurred the wrath of Mr. Trump and a mob of his supporters when he refused to carry out Mr. Trump’s demand that he block the certification of the 2020 election results.

“During my presidential campaign, I made it clear that there were profound differences between me and President Trump on a range of issues, and not just our difference on my constitutional duties that I exercised on January the 6th,” he said.

Mr. Pence said he was disappointed that Mr. Trump was no longer focused on reducing the national debt or on other issues that are important to conservatives.

“As I have watched his candidacy unfold, I’ve seen him walking away from our commitment to confronting the national debt,” he said in the interview. “I’ve seen him starting to shy away from a commitment to the sanctity of human life, and, this last week, his reversal on getting tough on China and supporting our administration’s effort to force a sale of ByteDance TikTok application.”