Investors were also eyeing testimony this week from the head of the Federal Reserve about the state of the US economy and the likely timeline for raising interest rates as the central bank winds down its five-year stimulus campaign.
Tokyo stocks gained 0.88%, or 132.78 points, to finish at 15,296.82, snapping a five-day losing streak, as the weaker yen helped lift the market.
Sydney rose 0.45%, or 24.6 points, to 5,511.4, Seoul added 0.26%, or 5.14 points, to 1,993.88 and Shanghai climbed 0.96%, or 19.69 points, to end at 2,066.65.
Hong Kong was 0.46% higher in the afternoon.
Regional sentiment was supported by gains on Wall Street on Friday as fears receded over the health of a troubled Portuguese bank that rocked markets late last week.
The focus turned to China, which is due to release second-quarter GDP figures on Wednesday along with other data including industrial production and retail sales numbers.
Recent concerns over economic prospects for China — a key driver of world growth — have eased owing to a pick-up in key indicators in the second quarter and government stimulus measures to boost the economy.
But an AFP survey predicted that growth failed to accelerate in the three months to June, with the economy forecast to record its worst annual performance in 24 years.
China's GDP expanded 7.4% year-on-year in that period — a result that would put it in line with the first quarter's expansion — according to the median forecast in the survey of 17 economists.
Investors will also be watching US retail sales data and the minutes from the Reserve Bank of Australia's policy meeting, which are both out on Tuesday. On Thursday, US housing starts data will be released.
Federal Reserve chief Janet Yellen will deliver the central bank's semi-annual report on the economy and monetary policy to Congress in hearings Tuesday and Wednesday. Investors will be watching for clues on the direction of the economy and the outlook for raising interest rates.
US stocks ended slightly up on Friday following a handful of mixed earnings reports in the coming week and as officials in Lisbon took steps to allay fears of a possible banking crisis.
Troubles at Portugal's largest listed lender, Banco Espirito Santo, had raised fears of a possible default and a return to the dark days of the eurozone debt crisis.
The Dow Jones Industrial Average rose 0.17% to 16,943.81 Friday and the broad-based S&P 500 gained 0.15% to 1,967.57.
On oil markets US benchmark West Texas Intermediate for August delivery was down 53 cents at $100.30 in afternoon trade and Brent crude for August shed 19 cents at $106.47
The dollar changed hands at 101.40 yen in Monday afternoon Tokyo trade, up from 101.23 yen in New York on Friday afternoon.
And the euro bought $1.3602 and 137.95 yen against $1.3604 and 137.78 yen in US trade.
Gold fetched $1,321.37 an ounce at 1045 GMT compared with $1,335.62 late Friday.
In other markets, Mumbai fell 0.07% to end at 25,006.98 points. Gitanjali Gems fell 5.58% to 73.55 rupees, while Mcleod Russel India fell 5.46% to 283.90 rupees.
Jakarta fell 0.23%, or 11.54 points, to 5,021.06
Bank Negara Indonesia lost 0.50% at 5,025 rupiah, while Hero Supermarket gained 0.72% at 2,800 rupiah.
Singapore fell 0.08%, or 2.75 points, to 3,290.98.
Singapore Telecom was unchanged at S$3.88 and banking giant DBS climbed 0.06% to S$17.18.
Kuala Lumpur rose 0.09%, or 1.72 points, to 1,884.87.
Telekom Malaysia added 0.96% to 6.34 ringgit, Public Bank rose 0.20% while RHB Capital lost 0.65% to 9.12 ringgit.
Wellington rose 0.53%, or 27.27 points, to 5,127.87. Trade Me was up 0.57% at NZ$3.55 and Telecom Corp climbed 1.29% to NZ$2.75.
Taipei gained 0.26%, or 24.46 points, to 9,520.3. Taiwan Semiconductor Manufacturing Co was 0.75% lower at T$132.5 while Cathay Financial Holding gained 4.5% to T$50.