The Shanghai Composite index added 0.4% to 2,952.99, while Hong Kong's Hang Seng rebounded from losses that followed clashes between protesters and police over the weekend, gaining 0.3% to 28,178.88. In South Korea, the Kospi gained 0.5% to 2,040.58.
Australia's S&P ASX 200 advanced 0.3% to 6,846.40. Shares fell in Taiwan and Bangkok but rose in Singapore and Jakarta. The U.S. and China head into another round of trade negotiations on Tuesday. Investors are hoping Beijing and Washington can avoid another escalation in tariffs like the one that occurred two months ago after talks fell apart.
The gains in Tokyo came despite news that industrial production sank 3.6% from the month before in June. Given uncertainties over global demand and trade disputes, economists have been downgrading their growth forecasts, with the BOJ cutting its own annual growth estimate for the current year by 0.1% to 0.7%.
"The Bank of Japan struck a dovish tone today, promising further easing measures if needed. But we still think it will refrain from lowering interest rates any further," Marcel Thieliant of Capital Economics said in a commentary.
Major U.S. stock indexes closed mostly lower Monday as investors turned cautious ahead of a key Federal Reserve interest policy announcement and other potentially market-moving developments on tap for this week. That includes the government's monthly jobs report for July, which will be released on Friday.
The S&P 500 index slipped 0.2% to 3,020.97. The Dow Jones Industrial Average rose 0.1% to 27,221.35 and the Nasdaq composite fell 0.4% to 8,293.33. The Russell 2000 index of smaller companies slid 0.6% to 1,569.02.
Traders expect the Federal Reserve will cut its benchmark short-term rate on Wednesday to help ensure U.S. economic growth in the face of trade uncertainty. Investors are expecting the Fed will cut its rate by a quarter of a percentage point from its current range of 2.25% to 2.50%. That would be the Fed's first rate cut in a decade.
Investors also will be wading through a heavy slate of corporate earnings reports this week. Bond prices rose. The yield on the 10-year Treasury note fell to 2.06% from 2.08% late Friday. ENERGY: Benchmark crude oil rose 40 cents to $57.27 per barrel in electronic trading on the New York Mercantile Exchange. It gained 67 cents to settle Monday at $56.87 a barrel. Brent crude oil, the international standard, gained 44 cents to $64.06 a barrel.
CURRENCIES: The dollar slipped to 108.63 Japanese yen from 108.78 yen on Monday. The euro strengthened to $1.1139 from $1.1145.
AP Business Writers Alex Veiga and Damian J. Troise contributed to this report.