President Trump on Monday began to confront the potential economic blowback from his military strikes on Iran, which threatened to send oil and gas prices soaring at a moment when U.S. consumers are already facing significant financial strains.

The mere prospect of rising energy costs appeared to spook even Mr. Trump, who took to social media to push for more domestic drilling while demanding that companies “KEEP OIL PRICES DOWN.” Otherwise, the president said, they would be “PLAYING RIGHT INTO THE HANDS OF THE ENEMY.”

“I’M WATCHING!” he added.

By Monday afternoon, global oil markets appeared relatively unfazed by the rising tensions between the two nations, just days after Mr. Trump dispatched U.S. bombers on a mission to disable three Iranian nuclear sites. Prices rose over the weekend but fell on Monday after Tehran launched retaliatory missile strikes against American bases abroad.

But it remained unclear if Iran would continue to respond, or if its leaders might escalate the conflict, particularly by trying to block access to the Strait of Hormuz, the narrow waterway that serves as the critical entrance point to the Persian Gulf. The world ships substantial amounts of oil and liquefied natural gas through the passage, so any interruption to commerce could cause energy prices to surge globally.

A spike in energy costs could prove especially difficult for American consumers and businesses this summer, given that it could arrive at about the same time that Mr. Trump plans to revive his expansive, steep tariffs on nearly every U.S. trading partner. Many economists expect those levies to push up prices after years of high inflation.

In April, the president announced, then suspended, the sky-high duties, seeking to quell a global market meltdown over his disruptive and legally contested campaign to remake global trade. But Mr. Trump has not wavered in his plan to implement the tariffs again on July 9, and many economists expect companies — which pay the duties when they source foreign products — to pass the added costs down to their customers.