(Corrects day in paragraph 1.)

By Wayne Cole

SYDNEY (Reuters) -Wall Street futures rose and the dollar eased in Asia on Tuesday after U.S. President Donald Trump said Iran and Israel had agreed to a ceasefire, sending oil prices into a deep dive as concerns over supply disruptions ebbed.

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

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

However, both Israel and Iran continued their missile strikes, making investors cautious about piling into risk assets just yet.

"This lifts some of the geopolitical uncertainty surrounding the markets, although, for the most part, equity investors have been kind of shrugging the uncertainty off," said Jack Ablin, chief investment officer at Cresset Wealth Advisors in Palm Beach, Florida.

"It certainly sounds like a significant milestone, and I hope it's true."

With the immediate threat to the vital Strait of Hormuz shipping lane seemingly over, U.S. crude futures fell another 4% to $65.75 per barrel.

S&P 500 futures gained 0.3% in early trade, while Nasdaq futures added 0.5%.

Nikkei futures traded up at 38,905, well above the cash close of 38,354.

Futures for 10-year Treasuries fell 6 ticks as the need for safe havens lessened, while interest rate futures slipped as investors rowed back a little on expectations for rate cuts.

The 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% chance the Fed will cut at its next meeting on July 30.

News of the ceasefire saw the dollar extend an overnight retreat and slip 0.1% to 145.92 yen, while the euro edged up 0.1% to $1.1589.

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.

The risk-on mood saw gold prices ease 0.4% to $3,353 an ounce.

(Editing by Sam Holmes)