The yen sank against the euro and the dollar after Japan's incoming prime minister again called on the central bank to take further steps to ease monetary policy, warning he would change the law to make sure it followed his instructions.
Hong Kong gained 0.20 percent, Shanghai was 0.43 percent higher and Seoul rose 0.11 percent.
Sydney ended 0.25 percent higher, adding 11.6 points to 4,635.2 and Wellington, which was open for just half a day, closed flat, edging up 3.08 points to 4,057.82.
Tokyo, Manila and Jakarta were closed for public holidays.
Regional gains came despite losses on Wall Street Friday as Capitol Hill broke up for Christmas without an agreement to avoid the huge tax hikes and spending cuts due to take effect in just over a week.
If the $600 billion package comes into effect and a less painful budget to cut the nation's deficit is not agreed, economists say it will tip the United States into recession, which would have a knock-on effect for the world economy.
Investors were hit after House Speaker John Boehner late Thursday scrapped a vote on a bill that would have extended tax cuts for all Americans earning less than $1 million even if a wider deal could not be struck.
The move, which he described as his "Plan B", was dropped because he did not have enough support. He said his party would recess until after Christmas.
"The breakdown of what little progress there was in the US has hit markets hard..., especially since Speaker John Boehner appears to have lost the support of part of his Republican party," said Chris Beauchamp, Market Analyst at IG Markets in Britain.
"While we haven't seen similar volatility to that experienced during the debt ceiling crisis (in August 2011) yet, the New Year could get messy if we cross that particular Rubicon" he told Dow Jones Newswires.
"Perhaps the only thing we can hope for is that (Federal Reserve) chairman Ben Bernanke will step into the breach to calm markets with some easing magic if 1 January comes and goes without a resolution," Beauchamp added.
On Wall Street the Dow lost 0.91 percent, the S&P 500 fell 0.94 percent and the Nasdaq dipped 0.96 percent.
However, the dollar improved on Monday against the yen after Shinzo Abe stepped up pressure on the Bank of Japan Sunday to set a two-percent inflation target.
The prime minister-elect told Fuji Television the bank's policy board must back his proposed two percent inflation goal in January and warned failure to do so would mean he would amend the law that sets out its duties and guarantees its independence.
The Japanese unit has already come under pressure as Abe, whose conservative Liberal Democratic Party won a landslide election last week, has said he will push the BoJ to carry out more aggressive easing measures.
In Asian trade the euro bought 111.22 yen, compared with 110.05 yen late Friday in New York, while it was also at $1.3182 from $1.3181.
The dollar fetched 84.40 yen, up from 84.25 yen.
Oil prices were lower, with New York's main contract, light sweet crude for delivery in February shedding 16 cents to $88.50 and Brent North Sea crude for February delivery falling eight cents to $108.89.
Gold was at $1,655.80 at 0255 GMT compared with $1,648.01 late Friday.