MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.5 percent.
Asian stocks rose on Monday, shaking off Wall Street's uninspiring performance on Friday, while sterling was mostly steady after a van rammed into pedestrians in London even as markets braced for the start of Brexit talks.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.5 percent.
Japan's Nikkei added 0.6 percent.
Australian shares climbed 0.5 percent and South Korea's KOSPI jumped 0.6 percent.
Chinese shares advanced 0.55 percent after data showed home prices rose 10.4 percent in May from a year ago, although slowing from April's 10.7 percent gain.
Hong Kong's Hang Seng gained 0.85 percent.
"Generally, the environment still remains fairly positive for risk appetite," said Khoon Goh, head of Asia research at Australia and New Zealand Banking Group in Singapore.
"Now that the (Federal Reserve interest rate decision) is out of the way, the focus, for this region anyway, will remain on whether the economic environment will stay positive and the recovery will continue."
On Friday, Wall Street ended mixed, with energy names offsetting declines in consumer stocks, which were clobbered by Amazon.com's $13.7 billion deal to buy upscale grocer Whole Foods Market.
The S&P 500 index closed flat, the Dow Jones Industrial Average ended up 0.1 percent and the Nasdaq lost 0.2 percent.
Europe, however, had a more upbeat session on Friday, with British, German and French stocks, as well as the broader STOXX Europe 600, all closing higher.
The British pound fell almost 0.1 percent to $1.2769 from late Friday levels in New York after a van rammed into worshippers as they were leaving Finsbury Park mosque in North London early on Monday.
Police reported a number of casualties and said one person had been arrested.
Brexit Secretary David Davis starts negotiations in Brussels on Monday, which will be followed by a Brussels summit on Thursday and Friday where British Prime Minister Theresa May will encounter - but not negotiate with - fellow European Union leaders.
Davis's agreement to Monday's agenda led some EU officials to believe that May's government may at last be coming around to Brussels' view of how negotiations should be run for Britain's exit from the EU. May's own immediate political survival is in doubt after she lost her parliamentary majority in an election.
Polls showing a strong parliamentary majority for French President Emmanuel Macron following Sunday's vote, giving him a powerful mandate to push through his pro-business reforms, lent support to the euro.
The common currency was steady at $1.11965, retaining Friday's 0.5 percent gain.
The dollar was subdued after U.S. homebuilding fell for a third month in May to the lowest in eight months and a barometer of U.S. consumer sentiment unexpectedly fell in early June, prompting concerns about the Federal Reserve's plans to stick with its monetary policy tightening.
The dollar index, which tracks the greenback against a basket of six global peers, was unchanged at 97.167, failing to make up any of Friday's 0.3 percent loss.
The market is awaiting comments by New York Fed President William Dudley, a close ally of Fed Chair Janet Yellen, when he speaks at a business roundtable in New York state.
"In the wake of Friday's weak U.S. data, Dudley could provide insight into whether the Fed is still poised to continue normalising monetary policy," said Masafumi Yamamoto, chief forex strategist at Mizuho Securities in Tokyo.
"My view is that Dudley won't sound too dovish, and thus allow the dollar's gradual rise to resume."
The greenback fared better against the Japanese yen , which remained weak after the Bank of Japan left its ultra-loose monetary policy unchanged last week.
Data on Monday showing Japanese exports rose at their fastest pace in May since January 2015 failed to lift the yen.
The dollar added 0.1 percent to 111.01 yen, after touching a two-week high on Friday.
In commodities, oil futures lingered near six-week lows, as concerns about a supply glut amid faltering demand.
U.S. crude slipped 0.45 percent to $44.55 a barrel, while global benchmark Brent dropped 0.4 percent to $47.17.
Gold touched a 3-1/2-week low earlier in the session, and was trading down slightly at $1,252.20 an ounce at 0158 GMT.
(This article has not been edited by DNA's editorial team and is auto-generated from an agency feed.)
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