(BSS/AFP) - Oil prices rallied and stock markets mostly fell Tuesday as markets digested the lack of progress towards Middle East peace and awaited a US-China summit.

Iran`s chief negotiator said Tuesday that Washington must accept Tehran`s latest peace plan or face failure.

"The longer they drag their feet, the more American taxpayers will pay for it," Mohammad Bagher Ghalibaf said in a post on X.

Trump, on his way towards Beijing, said he expected a "long talk" with counterpart Xi Jinping about Iran, which relies on China as the top customer for its US-sanctioned oil.

But he also played down disagreements on Iran, saying that Xi has been "relatively good, to be honest with you."

"I don`t think we need any help with Iran. We`ll win it one way or the other. We`ll win it peacefully or otherwise," Trump told reporters as he left the White House.

But the lack of progress means the Strait of Hormuz remained largely closed to tanker traffic. The international benchmark Brent North Sea crude and the main US contract, West Texas Intermediate, both rose more than three percent.

Meanwhile, the latest consumer price index data in the United States confirmed that high energy prices are stoking inflation, with the index recording the largest annual gain in nearly three years in April.

CPI rose 3.8 percent year-on-year, up from March`s 3.3 percent figure, the US Bureau of Labor Statistics said.

Analysts see the report as dimming the odds for Federal Reserve interest rate cuts this year.

The inflation report weighed on Wall Street stocks throughout the session, but major indices finished well above session lows. The S&P 500 finished at 7,400.96, down 0.2 percent after earlier losing around one percent.

"The market remains calm," said Mabrouk Chetouane, head of global markets at Natixis, adding that investors believe Washington and Tehran will reach an agreement before too long.

Markets are also optimistic about the upcoming US-China summit, Chetouane said, while noting that any additional tariffs after the meeting would be an unwelcome surprise.

"Stability is essential for the capital markets," he said.

Europe`s main stock markets ended the day in the red after losses for some major Asian indices.

In Britain, the yield on the country`s 30-year bonds reached 5.814 percent Tuesday, the highest level since 1998.

The rise in yields reflects political uncertainty as Prime Minister Keir Starmer clings to power.

More than 80 of Labour`s 403 members of parliament have now called for Starmer to quit immediately or to set out a timetable for his departure.

On Tuesday, more than 100 Labour members of parliament signed a statement backing their leader, highlighting the deep divisions within the beleaguered ruling party.

In South Korea, calls for a social tax on artificial intelligence profits largely dragged down the tech-rich Kospi index by five percent.

South Korea is riding a chip boom driving massive earnings for tech giants Samsung and SK hynix, which had sent the Kospi to record highs in recent weeks.

- Key figures at around 2020 GMT -

Brent North Sea Crude: UP 3.4 percent at $107.77 a barrel

West Texas Intermediate: UP 4.2 percent at $102.18 a barrel

New York - DOW: UP 0.1 percent at 49,760.56 points (close)

New York - S&P 500: DOWN 0.9 percent at 7,400.96 (close)

New York - Nasdaq Composite: DOWN 0.7 percent at 26.088.2 (close)

London - FTSE 100: DOWN less than 0.1 percent at 10,265.32 (close)

Paris - CAC 40: DOWN 1.0 percent at 7,979.92 (close)

Frankfurt - DAX 30: DOWN 1.6 percent at 23,954.92 (close)

Tokyo - Nikkei 225: UP 0.5 percent at 62,742.57 (close)

Hong Kong - Hang Seng Index: DOWN 0.2 percent at 26,347.91 (close)

Shanghai - Composite: DOWN 0.3 percent at 4,214.49 (close)

Euro/dollar: DOWN at $1.1745 from $1.1783 on Monday

Pound/dollar: DOWN at $1.3542 from $1.3610

Dollar/yen: UP at 157.57 from 157.19 yen

Euro/pound: UP at 86.70 pence from 86.58 pence