Japan's Nikkei led the way as a rise of 0.5 percent cleared a peak from 2000 to reach ground last trod in late 1996.
MSCI's index of Asia-Pacific shares outside Japan edged up 0.13 percent to bring its gains over the past six sessions to about 2.9 percent.
In China, official efforts to calm jittery investors seem to have steadied sentiment after steep losses last week. Shanghai stocks were up 1.6 percent but trade remained volatile.
Gains on Wall Street had been minor, though still enough to see the Nasdaq to a record peak. The Dow ended Tuesday up 0.13 percent, while the S&P 500 added 0.06 percent and the Nasdaq 0.12 percent.
Risk appetites were whetted after Greece's leftwing government expressed confidence that parliament would approve a debt deal with lenders, despite an angry reaction from some of its own lawmakers.
EU finance ministers meet on Wednesday to discuss whether or not to put the plan to euro zone state heads. If it goes ahead, the Greek parliament could vote as early as this weekend.
Bond investors were encouraged enough to push down yields on Greek 10-year debt by 60 basis points, with yields in Italy and Portugal following.
Yields went the other way in the United States following a string of generally upbeat economic data and comments from Fed Governor Jerome Powell that the economy could be ready for interest rate increases in both September and December.
That was unwelcome news for debt markets which are priced for only one hike this year. Yields on 10-year Treasury notes duly rose to their highest in 1-1/2 weeks at 2.43 percent.
"Markets appear to have interpreted the prospect of a deal between Greece and its creditors as removing a source of uncertainty, which may allow the Fed to commence hiking interest rates in September," said analysts at ANZ.
All of which helped give the U.S. dollar index its biggest daily gain since late May.
The greenback was particularly strong against the euro, which had peeled off to $1.1176 from a $1.1410 top at the start of the week. Against the yen, the euro was down at 138.34, having fallen from 140.
The dollar was also firm at 124.86 yen and well above the recent trough of 122.46.
In commodity markets, oil prices rebounding ahead of U.S. inventory data expected to show strong demand for gasoline.
U.S. crude futures added 11 cents to $61.12 a barrel, while Brent rose 10 cents to $64.55.
Gold slipped on the firmer dollar to reach $1,176.90 an ounce.
source: interaksyon.com
