Japan's Nikkei share average shed 0.7% to a near four-week low after the US S&P 500 overnight suffered its ninth loss in 11 sessions, while oil prices remained on the back foot.
President Barack Obama met with Republican and Democrat leaders in Congress but reiterated in a speech that he would not give in to Republican demands to roll back his healthcare programme in exchange for reopening the government.
The benchmark S&P 500 index shed 0.9%, although it climbed off its lows after the New York Times reported that House Speaker John Boehner told colleagues that he would not let the United States default on its debt.
The debt ceiling is far more important than a partial US government shutdown, which began on Tuesday, since it could lead to an unprecedented default by the United States, an outcome the market assumes is unthinkable.
BNP Paribas analysts said it was increasingly possible that the standoff would continue until the debt ceiling deadline on October 17.
"Market reaction is likely to intensify going into that date however, with the dollar extending its slide versus yen, Swiss franc and the euro," they wrote in a note.
"The silver lining for the dollar is that it is already trading at a sizeable discount relative to short-term rates, suggesting that there will be plenty of scope for the dollar to rally on any positive outcome in Washington."
The shutdown has caused a delay in the release of the closely-watched nonfarm payrolls data, normally due out on Friday. The data is a key piece of information for the Federal Reserve to consider when deciding to scale back its stimulus.
The dollar was also hurt by slower growth in the US services sector in September.
The euro was steady at $1.3622 in early Asian trade, not far from an eight-month high of $1.36465 touched on Thursday. The common currency was also aided by the European Central Bank's apparent lack of concern over the euro's recent strength and better-than-expected euro zone data.
Against a basket of major currencies, the greenback was near an eight-month trough.
The dollar stood at 97.38 yen, ahead of the outcome of a two-day Bank of Japan policy meeting, after hitting a five-week low of 96.93 on Thursday.
The BOJ is expected to maintain its massive stimulus and reiterate its upbeat view that the economy is strong enough to weather a sales tax increase next year without additional monetary policy measures.
MSCI's broadest index of Asia-Pacific shares outside Japan held steady near a one-week high and Seoul shares were flat, supported by a 0.9% gain in Samsung Electronics Co Ltd after estimating its July-September earnings rose 25% to a record $9.4 billion, ahead of analysts' expectations.
Brent crude slipped 0.2% to around $108.8 a barrel, adding to a 0.2% decline overnight, as the slower service sector growth in September compounded worries about raw materials demand due to the US budget crisis and government shutdown.
Copper prices edged 0.3% higher, recouping some of Thursday's 1.3% tumble.