Trump has faced intense political pressure to end the conflict, and critics have pointed to the cost, which Pentagon chief Pete Hegseth said on Tuesday had soared to US$37.5 billion.
But Trump on Wednesday rejected polls showing the war was unpopular with voters as he headed to an airbase for the return of the remains of three US troops killed in recent Iranian attacks.
"Americans don't want high gasoline prices but they're not against the war," he said.
Brent Crude, the global oil benchmark, briefly topped US$95 a barrel for the first time in six weeks on Wednesday. Crude futures later shed some of the gains, but were still up about three per cent.
PICKAXE MOUNTAIN
The US military said it had launched an eleventh consecutive night of strikes intended to "further degrade Iran's ability to threaten commercial shipping in the Strait of Hormuz".
Trump had said earlier that the next US target could be an
underground complex known as Pickaxe Mountain
, or Kolang in Persian, a site near Natanz where Western intelligence agencies suspect Iran is building an undeclared nuclear enrichment facility.
Iran threatened reprisals, with the Khatam Al-Anbiya military command saying it would strike "all the interests of America, the allies and supporters" if such an attack were carried out, the state broadcaster reported.
Foreign ministry spokesman Baqaei, meanwhile, insisted that "Washington's obsessive focus on Kolang Kouh where no nuclear activity is taking place is nothing more than a fabricated pretext for aggression".
The threats came as Tehran pressed its attacks on targets in US-allied Gulf states.
Kuwait's army said its air defences were engaging drones from Iran, while Jordan said it had shot down four missiles and four drones.
Air alert sirens also sounded in Bahrain, with an AFP correspondent in Manama hearing an explosion.
The Iranian military and its powerful Revolutionary Guards confirmed targeting US assets in all three countries.