It came after an Iranian missile brought down an unmanned US drone on Thursday. Tehran said it shot it down over its territory, whilst Washington insisted it was flying in international airspace.
U.S. President Donald Trump has claimed he aborted a military strike on Iran because it could have killed 150 people.
The strike would have been in retaliation for Iran's shooting down of an unmanned US surveillance drone on Thursday which Tehran claimed was flying over its territory.
But the US insists the downed drone was flying in international airspace.
"They shot down an unmanned drone, plane, whatever you want to call it," he told NBC, a US news channel.
"And here we are sitting with a hundred and fifty dead people that would have taken place probably within a half an hour after I said go ahead'. And I didn't like it. I didn't think it was - I didn't think it was proportionate."
Iran's airforce commander claimed that a US military plane carrying passengers was in sight near the drone but that he refrained from targeting it.
"While we were tracking the spy drone there was also a P-8 spy plane with 35 crew on board which we could have shot at, but we did not do so," Amir Ali Hajizadeh said.
The show of restraint from both sides may be encouraging for now, but the threat of war between Iran and the United States, or at least a military escalation, is clearly unnerving the region.
Some international airlines are now re-routing their flights. That comes after the US Federal Aviation Administration stopped American airlines flying over the Strait of Hormuz and the Gulf of Oman on Thursday.
The narrow waterway is vitally important to the global economy — about a fifth of the world's oil supplies pass through it in giant tankers.