While Trump signalled he could wind down the war within weeks even without a deal, he also scaled up threats to pull the United States out of the NATO defence alliance if European states did not help stop Iran blocking the Strait of Hormuz.
"I was never swayed by NATO. I always knew they were a paper tiger, and (Russian President Vladimir) Putin knows that too, by the way," Trump told Britain's Daily Telegraph, saying he had moved beyond merely reconsidering US membership.
The remarks on the war underscored Washington's shifting and at times contradictory statements about a conflict that has killed thousands, spread across the region and caused unprecedented energy disruption.
"We'll be leaving (the Iran conflict) very soon," Trump told reporters, saying that could be "within two weeks, maybe two weeks, maybe three".
"Iran doesn't have to make a deal, no," he said, when asked if successful diplomacy was a prerequisite for the US to end what it calls "Operation Epic Fury".
International Energy Agency head Fatih Birol said the main issue from Iran's effective closure of the major global energy shipping route, the Strait of Hormuz, was the lack of jet fuel and diesel.
"We are seeing that in Asia, but soon, I think, in April or May, it would come to Europe," Birol told a podcast with Nicolai Tangen, the head of Norway's sovereign wealth fund.
The loss of oil in April would be twice that lost in March, he said.
Businesses around the world have been hit by the conflict, with cosmetics and tea among the latest sectors to report pain.
The United States had previously threatened to intensify operations if Tehran did not accept a 15-point US ceasefire framework demanding that Iran not pursue nuclear weapons or uranium enrichment and fully reopens the Strait of Hormuz.
The White House said Trump would address the nation "to provide an important update on Iran" on Wednesday (12pm on Thursday AEDT).
Rubio told Fox News there was potential for a "direct meeting at some point" and the United States could "see the finish line".
"It's not today, it's not tomorrow, but it is coming," Rubio said.
