SINGAPORE, April 28 (Reuters) - Asian stocks held near record highs and the dollar was muted on Tuesday as investors weighed the geopolitical maelstrom in the Middle East and braced for megacap earnings and a slate of central bank meetings, with the Bank of Japan due later in the day.

While the U.S. was reviewing Tehran's latest proposal to resolve the war in the Middle East, a U.S. official said President Donald Trump was unhappy with the proposal because it did not address Iran's nuclear program.

That leaves the two-month-long conflict in a stalemate with energy and other supplies through the critical Strait of Hormuz at a standstill.

MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.12%, hovering near the record high it touched on Monday. The index is on course for a 17% rise in April after dropping 13.5% in March.

Japan's Nikkei was down 0.5% after scaling a fresh record peak in the previous session. The S&P 500 eked out modest gains on Monday, poised for about 10% gain for the month. U.S. stock futures were 0.1% higher in Asian hours on Tuesday.

Global monetary policy will be in the spotlight this week as the BOJ, the U.S. Federal Reserve, the Bank of England and the European Central Bank are due to announce policy decisions. All are expected to stand pat on rates but attention will be on comments from policymakers on the impact of the war on prices.

The BOJ is widely expected to hold off raising interest rates on Tuesday, but drop hawkish signals to leave itself scope to push up borrowing costs in coming months to counter inflationary pressure from the Middle East conflict.

Markets are focusing on the BOJ's quarterly outlook report and comments from Governor Kazuo Ueda for clues on how the protracted Iran war affects its rate-hike path.

The yen was at 159.33 per U.S. dollar, still near the 160 level that traders have been worried about as a breach beyond it might spur Tokyo to step in to support the currency. The yen has been straddling 159 since early March.

"The BOJ is likely to stay highly sensitive to market volatility," said Fred Neumann, chief Asia economist at HSBC. "Our base case remains one single 25 basis point hike this year in July, but a June rate rise becomes more likely if the Strait of Hormuz is still effectively closed after mid-May."

The euro was steady at $1.1725, with the dollar index, which measures the U.S. currency against six major units, at 98.452.

The dollar benefited in March from safe-haven flows as the war erupted but shed most of those gains on hopes of a peace deal this month. It has steadied in recent days after U.S.-Iran talks stalled.

The war has also sent oil prices surging, fuelled inflation and cast a shadow over the outlook for global growth, with the closure of the strait, which normally carries a fifth of global oil and gas shipments, a key risk.

Brent crude futures edged up to $108.13 a barrel, near a three-week high. U.S. West Texas Intermediate was at $96.48. Oil prices are well above the pre-war levels but have come down from their peak on hopes for a peace deal. [O/R]

Investors are also focusing this week on earnings from tech giants Microsoft, Alphabet, Amazon, Meta Platforms and Apple that will be a test for the blistering AI-driven rally in April.

Anthony Saglimbene, chief market strategist at Ameriprise, said the earnings will provide the market with a real-time read on whether AI investment is translating into commercial results.

"The divergence between equity market optimism and the more cautious signals from bond and oil markets, however, reinforces the view that geopolitical developments remain an active and important variable in risk management," said Saglimbene.