Writing on his Truth Social site, Trump implied a ceasefire would go into effect in 12 hours, after which the war would be considered "ended".

A senior Iranian official confirmed Tehran had agreed to the ceasefire with Israel. Israel's Channel 12 reported Prime Minister Benjamin Netanyahu had agreed in a conversation with Trump to a ceasefire as long as Iran stopped its attacks.

Oil prices fell almost 4 percent, having already slid 9 percent on Monday when Iran made a token retaliation against a US base, which came to nothing and signalled it was done for now.

With the immediate threat to the vital Strait of Hormuz shipping lane seemingly over, US crude futures fell another 3.4 percent to $66.24 per barrel, the lowest since June 11.

"To the extent that we've got a reduction in the risk of a renewed oil price spike, I think that plays positively from a risk point of view. I think it sort of removes that downside global growth risks," said Ray Attrill, head of FX strategy at the National Australia Bank.

"I think that would encourage people in the view that maybe the US dollar can sort of resume its downtrend here and that."

Risk assets rallied, with S&P 500 futures up 0.5 percent and Nasdaq futures 0.7 percent higher. EUROSTOXX 50 futures jumped 1.1 percent and FTSE futures rose 0.3 percent.

The MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.8 percent while Japan's Nikkei rallied 1.3 percent.

News of the ceasefire saw the dollar extend an overnight retreat and slip 0.3 percent to 145.70 yen, having come off a six-week high of 148 yen overnight. The euro rose 0.2 percent to $1.1594 on Tuesday, having gained 0.5 percent overnight.

The yen and euro benefited from the slide in oil prices as both the EU and Japan rely heavily on imports of oil and liquefied natural gas, while the United States is a net exporter.

Against its major peers, the US dollar index slumped 0.6 percent overnight and was last unchanged at 98.20.

Ten-year Treasury yields rose 1 basis point to 4.353 percent, while interest rate futures slipped as investors rowed back a little on expectations for rate cuts.

The Treasury market had rallied on Monday after Federal Reserve Vice Chair for Supervision Michelle Bowman said the time to cut interest rates was getting nearer as risks to the job market may be on the rise.

Fed Chair Jerome Powell will have his own chance to comment when appearing before Congress later on Tuesday and, so far, has been more cautious about a near-term easing.

Markets still only imply around a 22 percent chance the Fed will cut at its next meeting on July 30.

The risk-on mood saw gold prices ease 0.6 percent to $3,346 an ounce.