But shares in Hong Kong eased, extending last week's losing streak, with banks down on brokers' concern they may need to make provisions against exposure to debt in Dubai.
Shares in Australia and Japan climbed, while the MSCI index of Asian stocks excluding Japan <.MIAPJ0000PUS> was steady and S&P futures were up.
Investors welcomed solid earnings results from Oracle and (BlackBerry maker) Research in Motion over the weekend, as well as a weaker yen, said Norihiro Fujito, general manager of investment research at Mitsubishi UFJ Securities in Tokyo.
But trading volume is becoming thin as the year-end draws near and the market could easily turn south if the yen strengthens again.
The Nikkei average <.N225> rose 0.6 percent as stocks such as chip-tester maker Advantest Corp <6857.T> gained.
Upbeat results from Oracle and Research In Motion helped boost the Nasdaq <.IXIC> on Friday, which ended up 1.45 percent. The Dow Jones industrial average <.DJI> closed up 0.20 percent and the Standard & Poor's 500 Index <.SPX> rose 0.58 percent.
Australia's biggest carrier Qantas Airways Ltd rose more than 5 percent after forecasting a return to profit, helping buoy the main index <.AXJO>, which rose 0.4 percent.
Mining stocks rose on stronger metal prices, with BHP Billiton Ltd up 1.8 percent and Rio Tinto Ltd adding 0.1 percent.
Shares in Seoul <.KS11> were unchanged, although KB Financial <105560.KS> eased and Shanghai's key stock index <.SSEC> fluctuated, falling 0.6 percent in early trade.
The dollar held close to its highest point in more than three months against the euro as currency players anticipated more year-end short-covering in the U.S. currency until the Christmas break later this week.
A brighter outlook for the U.S. economy after stronger figures on the job market and retail sales earlier this month has helped the dollar pull back from a long-running downward trend.
The dollar may extend gains a little more as momentum buyers could chase the dollar up while it stays in an uptrend, said Masafumi Yamamoto, chief FX strategist for Barclays Capital in Japan.
The euro was steady at $1.4341 after dipping to $1.4262 on Friday, its lowest since early September. The dollar was unchanged at 90.40 yen, after touching its strongest level for six weeks on Friday.
U.S. crude futures edged down, paring Friday's 1 percent rise after news Iranian troops had partly withdrawn from a disputed oil area claimed by both Tehran and Baghdad, easing tensions between two major crude exporters. NYMEX crude for January delivery was down 6 cents at $73.30 a barrel.