Former Vice President Mike Pence filed paperwork on Monday declaring his presidential candidacy, embarking on a long-shot campaign against the former president he served under, Donald J. Trump.

Mr. Pence, who filed the necessary papers to run with the Federal Election Commission, has polled in the single digits in every public survey taken so far, well behind Mr. Trump, who has reshaped the Republican Party over the last seven years.

The former vice president is expected to formally announce his campaign at a rally outside Des Moines on Wednesday, a day after former Gov. Chris Christie is expected to enter the race and the same day Gov. Doug Burgum of North Dakota is set to join.

Mr. Pence is planning to campaign extensively in Iowa, the first nominating state and a place where his hard-line conservative positions on issues like abortion could appeal to evangelical voters.

Advisers to Mr. Pence, a former governor of Indiana, see Iowa as geographically hospitable to the brand of conservatism he practiced before the Trump era. And he is making the bet that enough vestiges of the old Republican Party remain to give his message broad appeal.

Mr. Pence, whom the celebrity-obsessed Mr. Trump used to refer to as “out of central casting,” was a stalwart supporter and defender of Mr. Trump over the latter half of the 2016 presidential campaign as his running mate, at a time when Mr. Pence was facing a difficult re-election effort in Indiana.

He was Mr. Trump’s most loyal advocate throughout their time in office together.

But Mr. Trump began a pressure campaign on Mr. Pence to thwart Joseph R. Biden Jr.’s Electoral College victory from being certified after Mr. Trump lost the 2020 election. Mr. Pence refused to use his ceremonial role overseeing the certification at the Capitol on Jan. 6, 2021, to advance Mr. Trump’s aims.

That day, a pro-Trump mob attacked the Capitol, with some of Mr. Trump’s supporters chanting, “Hang Mike Pence!” Since then, the split between the two has become irrevocable.