LONDON, May 11 (Reuters) - The dollar was steady on Monday after U.S. President Donald Trump rejected Iran's response to a U.S. peace proposal, sending oil prices higher and prompting renewed concerns that the conflict in the Middle East will drag on.

The U.S. dollar index, which measures the greenback's strength against a basket of six currencies, was little changed at 97.995.

Oil prices, meanwhile, jumped, with Brent crude up 3.6% at $104.94 a barrel, after President Donald Trump on Sunday rejected Iran's response to a U.S. proposal for peace talks, raising worries that the 10-week-old conflict may drag on.

Yet, markets still seem to believe that the conflict will be resolved, said Kenneth Broux, head of corporate research for FX and rates at Societe Generale.

"I think the reason for that may be the involvement of China," he said. "The summit with China and the U.S. later this week is, for me, the main event really," Broux said, pointing to the influence the two countries have in the Middle East.

TRUMP IN CHINA CLOSELY WATCHED 

Trump and Chinese President Xi Jinping are set to discuss Iran, Taiwan, artificial intelligence, nuclear weapons and critical minerals when they meet, according to U.S. officials.

Inflation and growth worries linked to higher oil prices, as well as any potential reaction from central banks, also continue to play on the market's mind, Broux said.

U.S. inflation data for April is due this week after the U.S. jobs report released Friday showed that non-farm payrolls increased 115,000 in April, almost twice as fast as expected. Those figures reinforced expectations the Federal Reserve would keep interest rates unchanged for some time.

The Fed held rates steady last month as expected, but the decision exposed its deepest split in decades, with three officials dissenting against signalling future rate cuts.

Factors that could weigh on the dollar "have become more elusive after hawkish Fed dissents, resilient U.S. data and continued stalemate in the Middle East," said Alex Loo, senior macro strategist at TD Securities in Singapore.

Elsewhere, China's yuan reached its strongest level against the U.S. dollar in more than three years at one point on Monday. The offshore yuan was last steady, trading at 6.7928 yuan per dollar.

Data earlier in the day showed China's producer prices smashed expectations to hit a 45-month high in April on rising global energy costs. That followed figures released over the weekend showing China's export growth accelerated last month as factories raced to meet AI-related demand.

The euro was down 0.1% at $1.1774, the yen slipped 0.3% to 157.11 yen per dollar and the British pound was 0.23% lower at $1.36.

In the UK, markets are closely watching any potential fallout from last week's local elections, which saw heavy losses for British Prime Minister Keir Starmer's Labour Party.

"While Labour losses were not quite as bad as feared, they have failed to quell speculation over a Labour leadership contest and a clear leftward drift in government policy," Chris Turner, ING's global head of markets, said in a note.