WASHINGTON—President Trump attacked the lawmaker heading up the House’s impeachment efforts, saying the chairman of the Intelligence Committee misrepresented the president’s conversation with Ukraine’s leader and calling on the Democrat to resign.

Mr. Trump tweeted Friday morning that Rep. Adam Schiff of California on Thursday had “fraudulently read to Congress” a version of a July 25 call with Ukraine’s president that is at the center of the growing crisis for the Trump administration. Mr. Trump said he “was supposedly reading...