WASHINGTON—Senate Finance Committee Chairman Orrin Hatch is ratcheting up pressure on President Donald Trump to reconsider his tariff policies, warning in a letter that GOP senators may be ready to risk a legislative confrontation with the president unless he reverses course on trade.

“As you are aware, members of the Senate are increasingly considering legislation to reduce trade authorities that Congress has delegated to the President,” the Utah Republican wrote in a letter obtained by The Wall Street Journal. “I am sympathetic...