The gains came after Republican leaders said Thursday they would vote to extend the government's borrowing authority for six weeks. A spokesman for President Barack Obama said he would "likely" sign a bill to increase the nation's ability to borrow money.
The Dow Jones industrial average soared more than 300 points Thursday, breaking a three-week funk in stocks.
The budget impasse has resulted in a partial shutdown of the U.S. government but the bigger worry has been a looming deadline for the U.S. to raise its borrowing limit. Without that authority from lawmakers, the government could default on its debts, sending shockwaves through the global financial system and economy.
Japan's Nikkei 225 stock average was up 1.6 percent at 14,427.45 and Hong Kong's Hang Seng added 1.3 percent to 23,236.71. Australia's S&P/ASX 200 climbed 1.6 percent to 5,226.60. China's Shanghai Composite Index rose 1.2 percent to 2,210.32.
Markets were higher in Singapore, South Korea, India and elsewhere in the region.
"The noises out of Washington have begun to sound a little more encouraging," said Alastair McCaig, market analyst at IG.
Among individual stocks, Toyota Motor Corp. rose 1.1 percent in Tokyo after a U.S. jury ruled that the automaker is not liable for the death of a woman who was killed when her 2006 Camry apparently accelerated and crashed despite her efforts to stop.
The outcome of the lawsuit could influence whether Toyota should be held responsible for sudden unintended acceleration as part of a larger group of lawsuits filed in U.S. state courts following a series of massive recalls for quality defects.
In energy trading, benchmark crude for November delivery was down 25 cents at $102.75 a barrel in electronic trading on the New York Mercantile Exchange. The contract rose $1.40 to close at $103.01 on Thursday.
In currencies, the euro rose to $1.3535 from $1.3526 late Thursday. The dollar rose to 98.45 yen from 98.16 yen.