Tokyo opened up 1.16 percent, while Sydney dropped 0.90 percent. Seoul was up 1.23 percent. Hong Kong and Shanghai were among a number of markets closed for a public holiday.
Trading was thin in Japan, where the Golden Week holidays that began Friday were interrupted for a single day before the markets take another three days off.
"Investors are reacting calmly to negative earnings figures in Japan and there seems to be no fresh selling as they look beyond to the recovery expected at the latter half of the year," Hisatsune Kobayashi, a general manager at SMBC Nikko Securities told Dow Jones Newswires.
Strong US stocks were offsetting uncertainty on Japanese corporate earnings due to effects related to the March 11 earthquake and tsunami, another analyst said.
Stocks in Sydney were dragged lower by a rising Aussie dollar, which hit a new historic high of US$110.20 early Monday.
"The Aussie dollar is obviously a concern for the Australian share market at these levels," said MarketsPlus head of sales trading Scott Johnson. "We are waiting for potentially good results from the banks this week, but there's a little bit of apprehension in the broader market."
The US dollar was under pressure after the Fed said last week it had no timetable on raising interest rates and that loose monetary policy would continue.
The euro fetched $1.4821 in Tokyo morning trade, up from $1.4808 in New York late Friday. The European single currency stayed flat against the Japanese currency, trading at 120.30 yen.
The dollar traded at 81.19 yen, hardly changed from New York.
The Korean won was lifted to its highest level against the dollar in 32 months. The dollar fell past 1,070 won to hit 1,066.70.
In New York on Friday, US stocks rose modestly, with Dow blue chips spurred by Caterpillar's earnings while the Nasdaq struggled after lacklustre Microsoft results and a poor Research in Motion forecast.
Despite mixed economic data and a tumble in Microsoft shares, the New York Stock Exchange notched up its strongest monthly gain of the year.
The Dow Jones Industrial Average rose 47.23 points (0.37 percent) to finish at 12,810.54 while the tech-rich Nasdaq Composite edged up 1.01 points (0.04 percent) to 2,873.54.
In Tokyo, shares in Sony, which held an unusual Sunday news conference on a security breach, rose 1.90 percent to 2,302 yen in early trade.
Sony executives bowed in apology and said the company would begin restoring its shut-down PlayStation Network and Qriocity online services in the next week as it moved to improve security after the breach hit 77 million accounts.
Oil eased in Asian trade ahead of the release of a slew of key US economic data, analysts said.
New York's main contract, light sweet crude for June delivery, was down 68 cents to $113.25 from New York's close and Brent North Sea crude for June eased 43 cents to $125.46.