Japan's Nikkei stock average notched its first rise in five sessions on Tuesday (October 8).
That tracked gains in other Asian markets, but a lack of progress in ending the U.S. government shutdown and the debt-ceiling standoff kept investors on edge.
The benchmark Nikkei 225 closed up 0.3 percent at 13,894.61, rebounding from a five-week low of 13,748.94 hit earlier in the session.
South Korea's Kospi finished 0.42% higher or 8.34 points at 2,022.76.
The Shanghai Composite was trading 0.93% higher or 20.29 points to 2194.96.
Hong Kong's Hang Seng was trading 0.94% higher or 215.99 points to 23,189.94.