In an expletive-laden social media post on Sunday, Trump said the US would attack power plants and bridges unless the crucial waterway is open by Tuesday. BBC reported.
Brent crude rose above $110 (£83.38) a barrel before those gains eased after a report of US-Iran talks over a potential ceasefire.
Oil and gas shipments from the Middle East have been severely disrupted as Tehran threatens to attack vessels that try to use the strait in retaliation for US and Israeli airstrikes since 28 February.
News website Axios reported that the US, Iran and a group of regional mediators are discussing the terms of a potential 45-day ceasefire that could lead to a permanent end to the conflict, citing US, Israeli and regional sources.
BBC News has not verified the report. The White House did not immediately respond to a request fro comment.