"To my Republican friends, if we could work together in the last Congress, there is no reason we can’t work together in this new Congress," Biden, a Democrat, will say, according to excerpts of the speech released by the White House before the speech scheduled for 9 p.m.
One test of that challenge will be the White House push to raise the $31.4 trillion debt ceiling, which must be lifted in the coming months to avoid a default.
The White House has said Biden will not negotiate over that necessity; Republicans want spending cuts in exchange for their support.
He said he urged Biden not to use the phrase "extreme MAGA Republicans" in his speech, a reference to Trump's "Make America Great Again" slogan.
Some House Republican lawmakers have questioned Biden's victory in the 2020 presidential race against Trump, vowing to investigate his Cabinet and family.