WASHINGTON—President Trump said on Wednesday that he ordered Treasury Secretary Steven Mnuchin to substantially raise sanctions on Iran, the first U.S. policy response to last week’s attack on critical Saudi Arabian oil facilities.

The administration didn’t immediately say what steps it would take, but it can levy additional sanctions to cut off Iran’s remaining sources of revenue beyond the “maximum pressure” campaign that has already devastated Iran’s economy by blacklisting the country’s most important economic sectors.

“I have just instructed the Secretary of the Treasury to substantially increase Sanctions on the country of Iran!” the president said in a tweet.

Later, in comments to reporters in California, Mr. Trump said he was looking at various other options in responding to the strike and that further details on sanctions would be released in the next 48 hours.

The announcement of fresh sanctions may indicate the administration has chosen to stick with its primary strategy of economic warfare against Iran, forgoing a full-scale conventional military assault, say analysts and former officials.