The remarks underscored the shifting and at times contradictory statements from Washington about how the war, now in its fifth week, might end.
"We'll be leaving very soon," Trump told reporters at the White House on Tuesday, saying the exit could take place "within two weeks, maybe two weeks, maybe three".
Asked if successful diplomacy with Iran was a prerequisite to the US winding down what it has dubbed Operation Epic Fury, Trump said it was not.
"Iran doesn't have to make a deal, no," he said.
"No, they don't have to make a deal with me."
Earlier on Tuesday, US Defence Secretary Pete Hegseth said Trump was willing to make a deal with Iran to end the war that has killed thousands of people, spread across the region, disrupted energy supplies and threatened to send the global economy into a tailspin.
Iran's Revolutionary Guards hit back with a new threat against US companies in the region starting on Wednesday. It listed 18 businesses including Microsoft, Google , Apple, Intel, IBM, Tesla and Boeing .
Hegseth, who reported he visited troops in the Middle East on Saturday, said US was prepared to continue the war if Iran did not comply, he said.
"We have more and more options, and they have less ... in only one month we set the terms, the upcoming days will be decisive," Hegseth said in Washington on Tuesday.
"Iran knows that, and there's almost nothing they can militarily do about it."
Responding to the threat against American corporate interests, a White House official said the US military was "prepared to curtail any attacks".
Iranian Foreign Minister Abbas Araqchi on Tuesday said he has been receiving direct messages from US special envoy Steve Witkoff but they do not constitute negotiations, Qatar's Al Jazeera TV cited him as saying.
The messages include threats or exchanged views delivered through "friends", he said.
Trump on Monday threatened to obliterate Iran's energy plants if it does not agree to a peace deal and open the Strait of Hormuz, a vital waterway for global oil shipments that has effectively been blocked by Iran.
The US president on Tuesday criticised countries that have not helped the US war effort, such as Britain. In a social media post, he said that in response to the global fuel shortage, these countries should buy energy from the US or find "some delayed courage, go to the strait and just TAKE IT".
General Dan Caine, chairman of the Joint Chiefs of Staff, told reporters in Washington the US was further degrading and destroying Iran's capabilities.
He said the US military was continuing to strike key manufacturing and research sites and had taken out over 150 Iranian naval vessels. Hegseth said US strikes were causing widespread desertions in Iran.
With attacks showing no sign of easing, Pakistan is seeking to mediate in the war. The foreign ministers of China and Pakistan on Tuesday called for an immediate ceasefire, urging peace talks to be held as soon as possible after they met in Beijing.
Iran has remained defiant despite heavy US and Israeli attacks for the past month.
The Israeli military on Tuesday said it completed a wave of strikes targeting 20 weapons manufacturing sites and a research and development site in Iran.
with AP
