ABOARD AIR FORCE ONE/DUBAI, May 16 (Reuters) - U.S. President Donald Trump said Chinese President Xi Jinping had agreed Tehran must reopen the Strait of Hormuz, though China gave no indication it would weigh in.

Flying back from Beijing on Friday after two days of talks with Xi, Trump said he was considering whether to lift U.S. sanctions on Chinese oil companies buying Iranian oil. China is the biggest buyer of Iranian oil.

"I'm not asking for any favors because when you ask for favors, you have to do favors in return," Trump said when asked by a reporter on Air Force One whether Xi had made a firm commitment to put pressure on the Iranians to reopen the vital strait.

Xi did not comment on his discussions with Trump about Iran, although China's foreign ministry expressed frustration with the Iran war, calling it a conflict "which should never have happened, has no reason to continue."

'WE WANT THE STRAITS OPEN'

Iran effectively shut the strait, which carried one-fifth of the world's oil and liquefied natural gas supply before the U.S. and Israel launched attacks on February 28. The disruption to shipping has caused the biggest oil supply crisis in history, sending oil prices skyrocketing.

Thousands of Iranians were killed during the U.S. and Israeli air strikes, and thousands have been killed in Lebanon in renewed fighting there between Israel and the Iran-backed group Hezbollah.

The U.S. paused its attacks last month but began a port blockade. Tehran said it would not unblock the strait until the U.S. ended its blockade. Trump has threatened to resume attacks if Iran does not agree to a deal.

"We don't want them to have a nuclear weapon, we want the straits open," Trump said in Beijing, alongside Xi.

Iran, which has long denied that it intends to build a nuclear weapon, has refused to end nuclear research or relinquish its hidden stockpile of enriched uranium, to Trump's frustration.

Iranian Foreign Minister Abbas Araqchi said Tehran had received messages from the U.S. indicating Washington was willing to continue talks.

"We hope that, with the advancement of negotiations, we will reach a good conclusion so that the Strait of Hormuz can be completely secured and we can expedite the normalisation of traffic through the strait," he told reporters in New Delhi.

Trump, who told Fox News' "Hannity" program in an interview aired on Thursday that he was losing patience with Iran, said Tehran "should make a deal."

Oil prices rose around 3% to around $109 a barrel on Friday [O/R] on concerns over a lack of progress in resolving the conflict, while U.S. Treasury yields [US/] hit their highest in around a year on expectations the Federal Reserve might need to raise interest rates.

Talks on ending the war, which has become a liability for Trump ahead of U.S. congressional elections in November, have been on hold since last week when Iran and the U.S. each rejected the other's most recent proposals.

Iran would welcome Chinese input, Araqchi said on Friday, adding that Tehran was trying to give diplomacy a chance but did not trust the U.S., which has curtailed previous rounds of talks by launching air strikes.

(Reporting by Trevor Hunnicutt and Jana Choukeir, with additional reporting by Reuters Newsrooms; Writing by William Mallard; Editing by Tom Hogue)