Stocks held their ground and oil rose on Tuesday as investors weighed the stalemate in the Iran conflict, while the yen was steady after a hawkish split at the Bank of Japan underlined fears over the war's impact on inflation.

The United States was reviewing Tehran's latest proposal to resolve the war, even as a US official said President Donald Trump was unhappy with the plan as it did not address Iran's nuclear programme. That leaves the two-month-long conflict at an impasse, with energy and other supplies through the critical Strait of Hormuz still mainly shut, pushing oil prices above $110 a barrel on Tuesday.

Brent crude oil surged 2.7% to $111.20 a barrel, a three-week high, while US oil climbed 2.9% to $99.10.

Oil prices have steadily climbed in recent days as hopes ebb for an imminent peace deal, pushing up bond yields around the world in recent weeks.

Futures for the US benchmark S&P 500 stock index slipped 0.1%, and those for tech-focused Nasdaq fell 0.4%. European stocks dipped in early trading, but the STOXX 600 index was last flat.

Corporate results roll in

"Earnings season has helped markets look through the disruption, but the longer key oil flows remain constrained, the greater the risk that higher energy costs begin to bite," said Matt Britzman, senior equity analyst at Hargreaves Lansdown.

Read: War driven costs and opportunities

The US S&P 500 hit another record on Monday after rising for four weeks on optimism over a possible peace deal and ongoing excitement around AI.

Investors are focusing this week on earnings from tech giants Microsoft, Alphabet, Amazon, Meta Platforms and Apple which will test the blistering AI-driven rally.

Elsewhere, the dollar index climbed 0.2% as the pound and euro both slipped by the same amount. The dollar has been one of the few safe-haven assets during the Iran conflict, although it has given up much of its March gains in the last few weeks.

"The twists and turns of US-Iran peace negotiations continue to buffet markets," and doubts over the progress of peace talks was pushing the dollar higher, said Nick Rees, head of macro research at Monex Europe.

Bank of Japan split on rates

The BOJ left short-term rates unchanged on Tuesday at 0.75%, in the first of several central bank meetings this week that could shed light on the impact of the conflict.

"The 6–3 vote split and the stronger language on future policy adjustment suggest the bar for another hike may be falling," said Charu Chanana, chief investment strategist at Saxo.

Read More: The political economy of blockade

The yen initially strengthened but was last slightly lower at 159.53 per dollar, putting it near 160. A breach beyond that threshold has markets worried Tokyo might step in to support the currency. Japan's Nikkei stock index fell 1% from a record high hit on Monday.

Global monetary policy will be in the spotlight this week, with the US Federal Reserve, the Bank of England and the European Central Bank due to announce decisions after the BOJ. All are expected to keep rates unchanged, but attention will be on comments from policymakers on pricing pressure.