Attorney General Jeff Sessions is set to appear before the Senate Judiciary Committee on Wednesday morning, where he will likely face questions on contentious issues such as immigration, civil rights and his recusal from the investigation into Russia’s meddling in the 2016 election.

Democrats said they plan to push Mr. Sessions to describe his conversations with President Donald Trump, which he declined to discuss at his last appearance before a Senate panel in June. In that hearing, before the Senate Intelligence Committee,...