Tokyo's Nikkei 225, reopening after a national holiday, jumped 1.5% to 38,784.91 and the Kospi in South Korea surged 1.9% to 2,728.05.
Hong Kong's Hang Seng shed 0.9% to 18,420.38 and the Shanghai Composite index edged 0.1% lower, to 3,136.62. Data on travel, retail spending and home sales during the weeklong Golden Week holidays showed persisting weakness in the economy.
Australia's S&P/ASX 200 advanced 0.7% to 7,739.00 ahead of a central bank decision on interest rates.
Taiwan's Taiex was up 0.3%, while India's Sensex was nearly flat as the country began the third phase of its weeks' long national elections process.
On Monday, the S&P 500 rose 1% to 5,180.74. The Dow Jones Industrial Average added 0.5% to 38,852.27, and the Nasdaq composite jumped 1.2% to 16,349.25.
Tech stocks were at the forefront, with familiar ringleaders Nvidia and Super Micro Computer again pulling the market higher. They’ve had a couple hiccups recently, but a frenzy around artificial-intelligence technology has Nvidia up 86.1% for the year so far after Monday’s 3.8% gain. Super Micro is up 192.1% after its gain of 6.1%.
Berkshire Hathaway added 1% after Warren Buffett's company reported its latest quarterly results over the weekend.
It helped to offset a 9.7% slide for Spirit Airlines, which reported a slightly worse loss than expected. The carrier said it’s facing increased competition in many of its markets, particularly between the United States and Latin America.
Apple slipped 0.9% after Berkshire Hathaway revealed it had pared its stake in the tech giant.
The U.S. stock market has been swinging since setting a record at the end of March. It sunk for weeks on fears that stubbornly high inflation would prevent or at least delay the Federal Reserve from delivering the cuts to interest rates that Wall Street craves.
But markets found a burst of optimism at the end of last week following a cooler-than-expected jobs report. It suggested the U.S. economy could nail the tightrope walk of staying strong enough to avoid a bad recession, but not so firm that it puts too much upward pressure on inflation.
Goldman Sachs economist David Mericle said he still expects two cuts to rates this year, in July and November, after Fed Chair Jerome Powell "pushed back strongly against the possibility of further rate hikes" at his press conference last week.
This week is relatively quiet. The bulk of companies in the S&P 500 have already reported their results for the first three months of the year, with more than three-quarters topping profit expectations, according to FactSet.
But several more big names are still on the way, including The Walt Disney Co. and Uber Technologies.
In the bond market, which has been dictating much of the action in the stock market recently, Treasury yields held mostly steady.
The yield on the 10-year Treasury edged down to 4.49%, from 4.50% late Friday. The two-year Treasury yield, which more closely tracks expectations for the Fed, was also relatively little changed.
Traders are betting on a nearly 89% chance that the Fed will cut its main interest rate at least once before the end of the year, according to data from CME Group. That’s up from from an 81.6% probability seen a week earlier. Lower rates would help ease the pressure on the economy and financial system.
Corporate profit reports have been better than expected not just in the United States but also in Europe and Japan, according to strategists at Deutsche Bank. Global earnings growth is on track for a second straight quarter of growth following four consecutive declines.
In other trading, benchmark U.S. crude oil added 24 cents to $78.72 per barrel in electronic trading on the New York Mercantile Exchange. It gained 37 cents on Monday.
Brent crude, the international standard, was also up 24 cents at $83.57 per barrel.
The dollar rose to 154.49 Japanese yen from 153.90 yen. The euro was nearly unchanged at $1.0769.
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AP Business Writer Stan Choe contributed.
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