Donald Trump called for Iran's "unconditional surrender" as he warned supreme leader Ayatollah Ali Khamenei the US would not kill him "for now".
In a series of posts about the escalating Iran-Israel conflict on Truth Social, the president said "our patience is wearing thin" and told Tehran "we now have complete and total control of the skies over Iran".
It came as he convened a meeting of the National Security Council in the White House Situation Room on Tuesday afternoon, local time.
"We know exactly where the so-called 'Supreme Leader' is hiding," Mr Trump said. "He is an easy target, but is safe there — we are not going to take him out (kill!), at least not for now.
"But we don't want missiles shot at civilians, or American soldiers. Our patience is wearing thin. Thank you for your attention to this matter!"
Mr Trump's posts will heighten speculation about possible US involvement in the conflict.
Meanwhile, Iran warned of "punitive strikes" on Israel in retaliation to further overnight attacks.
Moments before the president's latest comments, US Vice-President JD Vance said that Mr Trump was prepared to "show restraint".
"The president has shown remarkable restraint in keeping our military's focus on protecting our troops and protecting our citizens," he said in a lengthy post on X.
"He may decide he needs to take further action to end Iranian enrichment. That decision ultimately belongs to the president."
He said "people are right to be worried about foreign entanglement" and criticised the past decades of US foreign policy.
"But I believe the president has earned some trust on this issue," he added.
Israel wants to target Iran's nuclear facility Fordo, which is believed to be only possible with American so-called bunker-busting bombs.
Meanwhile, the United States has deployed fighter jets to the region for defensive operations involving shooting down drones and projectiles, Reuters reported.
America is also extending the deployment of other warplanes in the region in a move US Defense Secretary Pete Hegseth has described as defensive in nature.
Trump signs on with G7 leaders
Meanwhile, Mr Trump signed a joint statement from G7 leaders in which they called for a "broader de-escalation of hostilities".
The US president made a sudden exit from the G7 summit in Canada overnight without putting his name to the statement and there had been speculation he would avoid signing altogether.
The statement, which has now been published, was released shortly before Mr Trump departed Kananaskis, Canada for Washington DC.
The Washington Post is reporting the language is slightly different to an earlier version seen by the publication — notably, that the final statement omits the line that called for both Iran and Israel "to show restraint".
The statement says the leaders "reiterate our commitment to peace and stability in the Middle East".
"In this context, we affirm that Israel has a right to defend itself. We reiterate our support for the security of Israel," it reads.
The G7 leaders — representing the US, France, the UK, Germany, Japan, Canada, Italy and the EU more broadly — signed the letter that said "Iran is the principal source of regional instability and terror".
"We have been consistently clear that Iran can never have a nuclear weapon," the document reads.
The leaders stopped short of calling for a ceasefire between Israel and Iran but said they "urge that the resolution of the Iranian crisis leads to a broader de-escalation of hostilities in the Middle East, including a ceasefire in Gaza".
On Air Force One on his way back to the US capital, Donald Trump spoke to reporters and said he was hoping for something "much better" than a ceasefire between Israel and Iran.
He said he was looking for "a real end", such as Iran "giving up entirely".
Earlier, French President Emmanuel Macron had told reporters Mr Trump leaving the G7 early was a good sign and Mr Trump had made an offer for a ceasefire between Israel and Iran.
"There is indeed an offer to meet and exchange. An offer was made especially to get a ceasefire and to then kick-start broader discussions," Mr Macron told reporters at the G7.
On Truth Social, Mr Trump said: "Wrong!"
"He has no idea why I am now on my way to Washington, but it certainly has nothing to do with a Cease Fire. Much bigger than that," the post read.
