WASHINGTON — President Trump plans to announce his nominee for the Supreme Court on Tuesday, moving to fill a seat held vacant for nearly a year by Senate Republicans and touching off what is expected to be a furious ideological showdown early in his administration.

Mr. Trump scheduled a prime-time televised announcement from the White House for 8 p.m. to present his choice to a national audience, his first foray into the judicial wars that have consumed Washington for generations. At least some Senate Democrats were already preparing to block anyone he picks.

The leading finalists were believed to be two federal appeals court judges with strong conservative records: Neil M. Gorsuch of the Denver-based 10th Circuit and Thomas M. Hardiman of the Third Circuit in Pittsburgh, according to Republicans close to the process. A third appeals court judge, William H. Pryor Jr. of the Atlanta-based 11th Circuit, has also been reported to be in the running.

Any Supreme Court nomination would raise partisan tensions, but this one is coming when Washington is already on edge over the fast-paced, sharp-edged beginning of Mr. Trump’s presidency. In particular, the capital is polarized over Mr. Trump’s executive order temporarily shutting the nation’s borders to refugees worldwide and to any visitors from seven predominantly Muslim countries.