U.S. President Donald Trump said on Monday that a "complete and total" ceasefire between Israel and Iran will go into force with a view to ending the conflict between the two nations, moments after both sides threatened new attacks.

Trump appeared to suggest that Israel and Iran would have some time to complete any missions that are underway, at which point the ceasefire would begin in a staged process.

"On the assumption that everything works as it should, which it will, I would like to congratulate both Countries, Israel and Iran, on having the Stamina, Courage, and Intelligence to end, what should be called, 'THE 12 DAY WAR'," he wrote on his Truth Social site.

According to Trump, Iran will initiate the ceasefire, followed by Israel 12 hours later, culminating in an official declaration of the war's end at the 24-hour mark.

Iranian Foreign Minister Seyed Abbas Araghchi posted on X on Tuesday that, "As of now, there is NO 'agreement' on any ceasefire or cessation of military operations." 

"However, provided that the Israeli regime stops its illegal aggression against the Iranian people no later than 4 am Tehran time, we have no intention to continue our response afterwards. The final decision on the cessation of our military operations will be made later."

Israel's Channel 12 reported that Israeli Prime Minister Benjamin Netanyahu agreed on Monday to a ceasefire so long as Iran stops firing.

Earlier Channel 12 said that Israel has sent messages to Iran that it is aiming for the air and missile war between the sides to end within days.

However, there was no immediate calm in the region. The Israeli military issued two evacuation warnings in less than two hours to residents of areas in the Iranian capital Tehran, one late on Monday and one early on Tuesday. 

Israeli Army radio reported early on Tuesday that alarms were activated in the southern Golan Heights area due to fears of hostile aircraft intrusion.

Trump's post came several hours after Iran launched a missile attack on an American air base that caused no injuries.

The attack on Al Udeid Air Base in neighboring Qatar threatened to widen a conflict that began on June 13 with an Israeli strike on Iran targeting its nuclear program and ballistic missiles.

Iran had threatened to retaliate against the U.S. after American B-2 stealth bombers dropped 30,000-pound bunker-busters on Iranian underground nuclear facilities at the weekend, joining Israel's air war against Iran, and Trump had raised the possibility of the Iranian government being toppled.

"We did not assault anyone, and we will never accept being assaulted by anyone," Iran's Supreme Leader Ayatollah Ali Khamenei said in a statement. "We will not submit to anyone's aggression – this is the logic of the Iranian nation."

Iran gave advance notice to the U.S. via diplomatic channels hours ahead of the attack, as well as to Qatari authorities, and Trump seized on that as a positive sign.

"I want to thank Iran for giving us early notice, which made it possible for no lives to be lost, and nobody to be injured," Trump wrote on his Truth Social media site. "Perhaps Iran can now proceed to Peace and Harmony in the Region, and I will enthusiastically encourage Israel to do the same."

The attack strained Iran's relationship with its Arab neighbors: Qatar condemned it, as did Bahrain, the United Arab Emirates, Saudi Arabia, Kuwait and Iraq.

(With input from agencies)