The KLSE's composite index has shot up to over 750 since hitting a low of 262.7 in September last year.
Shanghai's Composite index edged up by 15.17 points, or 0.6%, to 2, 373.21.
South Korea's Kospi Composite rose 0.8%, China's Shanghai Composite Index added 0.1% and Hong Kong's Hang Seng Index climbed 0.9%.
South Korea's Kospi Composite Index was off 0.1% while Singapore's Straits Times Index was up 0.2%.
In China, where Hong Kong's Hang Seng Index climbed 0.7% and the mainland's Shanghai Composite Index dropped 0.2%, investors were digesting a string of earnings reports from large Chinese companies.
Japan's Nikkei Stock Average jumped 2% to 9768.96, Hong Kong's Hang Seng Index rose 1.3% to 20900.73 and China's Shanghai Composite Index climbed 1.1% to 2420.28, all three rising for the first time this week.
In China, where Hong Kong's Hang Seng Index climbed 0.6% to 22251.15 and the mainland's Shanghai Composite Index ended down 0.1% at 2326.71, investors were digesting a string of earnings reports from large Chinese companies.
Hong Kong's Hang Seng Index climbed 0.3%, to 20741.45, while China's Shanghai Composite Index slipped 0.4%, to 2396.32.
China's Shanghai Composite Index lost 22% in 2011 as tighter government curbs on lending and investment cooled the country's rapid economic growth.
Now compare that to Shanghai in the same time, Shanghai's benchmark composite index rose 130 percent.
In Asia, China's Shanghai Composite Index fell 0.5% to a one-month low and declined 4.9% on the week.
China's Shanghai Composite Index, meanwhile, is up 2.4%, while the overall MSCI Asia index outside Japan is up 1.3%.
China's Shanghai Composite Index edged up 0.2% after data showing foreign direct investment flows into the country rose more than expected.
China's Shanghai Composite Index lost 1.4% to 2, 266.38 a day after it surged 4.2% in the wake of better-than-expected fourth-quarter economic data.
Most Asian markets extended declines, although China's Shanghai Composite Index bucked the trend by rising 0.6% after closing at a five-month low on Monday.
Reflecting such optimism (as well as a certain measure of irrational exuberance), China's Shanghai Composite Index holds a 140% gain for the past 52 weeks.
In Asia, China's Shanghai Composite Index climbed 1.4% as hopes of increased government spending on a wide range of investment projects lifted coal and construction companies.
China's Shanghai Composite Index lost 0.2% after news that industrial production for April and urban fixed-asset investment for the January-to-April period didn't rise as much as expected.
Markit's February composite purchasing managers index for the region was revised higher.
In America, the collapse is striking both for its severity and its breadth: home prices fell in every city covered by Case-Shiller's 20-city composite index in September.
On the first day of trading in the new year, America's high-tech Nasdaq Composite index fell 7.2% as investors worried about falling profits and the state of the economy.
South Korea's Kospi Composite rose 1% and Singapore's Straits Times Index was up 0.8%.
South Korea's Kospi Composite was down 0.4% and Singapore's Straits Times Index lost 0.3%.
South Korea's Kospi Composite was down 0.2% and Singapore's Straits Times Index lost 0.2%.
Elsewhere in the region, South Korea's Kospi Composite was off 0.4% and Singapore's Straits Times Index rose 0.2%.
China's Shanghai Composite rallied 1.8% after the manufacturing purchasing manager's index rose to 53.3 in April from 53.1 in March.
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