The remarks underscored Washington's shifting and at times contradictory statements about when and how a war that has killed thousands, spread across the region and caused unprecedented energy disruption might end.
"We'll be leaving very soon," Trump told reporters on Tuesday, 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.
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.
Attacks took place on multiple fronts early on Wednesday, with drones hitting fuel tanks at Kuwait's international airport causing a big blaze and authorities in Bahrain reporting a fire at an undisclosed company facility from an Iranian attack.
Qatar said an oil tanker leased to state-owned QatarEnergy was hit by an Iranian cruise missile in Qatari waters, with damage above the waterline but no injuries or environmental damage.
Explosions were heard in parts of Tehran after US-Israeli air attacks, according to Iranian state media.
State TV showed convoys of cars waving Iranian flags and pro-government rallies in several cities on a national day marking the establishment of the Islamic republic in 1979.
Shahid Haghani Port, Iran's largest passenger terminal, was hit by an overnight air strike but there were no casualties, deputy regional governor Ahmad Nafisi told state media, calling it a "criminal" attack on civilian infrastructure.
Iran has fired repeatedly on Gulf countries, some home to US bases, during the conflict, and its effective closure of the Strait of Hormuz has raised concern about its ability to use the vital waterway, a conduit for a fifth of global oil and liquefied natural gas, as a bargaining chip.
Higher oil and fuel prices are weighing on US household finances and are a political headache for Trump and his Republican Party before the November midterm elections.
US Defense Secretary Pete Hegseth said on Tuesday other countries needed to "be prepared to stand up" and help reopen the Strait of Hormuz, echoing criticism from Trump, who has singled out NATO members Britain and France.
Rubio told Fox News that Washington would not overlook the lack of assistance from other NATO members.
"After this conflict is concluded, we are going to have to re-examine that relationship," he said.
The United Arab Emirates is preparing to help the US and allies open the Strait by force, the Wall Street Journal reported.
Iran's Revolutionary Guards hit back with a new threat against US companies in the region, listing 18 businesses including Microsoft, Google, Apple, Intel, IBM, Tesla and Boeing.
Asked if he was concerned about threats, Trump said no.
Missile debris struck several areas in central Israel following an early-morning rocket volley from Iran.
Yemen's Houthis, who joined the regional war in recent days, said they carried out a missile attack on Israel, describing it as a joint operation with Iran and the Tehran-backed Hezbollah in Lebanon, the first such collaboration between them during the war.
Israel's military said air-defence systems were operating to intercept the threats.
