The South Korean won rose as much as 0.3 percent to 1,045.3 per dollar after the commerce minister said the government had no plans to curb the won's rise against the yen.
The won hit a seven-year high against the yen a week ago, raising concerns about the competitiveness of Korean exports and of intervention by authorities to stem the currency's gains.
The Taiwan dollar rose as much as 0.3 percent to 33.62 a dollar, helped by a return of foreign investors to the stock market. Foreigners, who sold a net 30.8 billion Taiwan dollars of stocks in October, have been net buyers for the last eight sessions.
The rupiah strengthened to nearly 10,000 per dollar, rising almost 1 percent from its levels on November 1 before local markets closed for Eid ul-Fitr holidays.
"People were caught long dollars during the holidays. They started selling as soon as the market opened," a Jakarta dealer said. "Around the 10,000 level we still see dollar demand from local corporates."
The Indonesian rupiah has lost 7.3 percent this year, making it is the worst performer in Asia after the Japanese yen.
But it has staged a comeback since hitting a four-year low of 11,750 per dollar on August 30, helped by the central bank raising interest rates to provide support and to battle inflation.
For its part, the government slashed fuel subsidies to reduce pressure on its budget and in an effort to cut costly fuel imports, which had caused the balance of payments to deteriorate.
The South Korean won, Taiwan dollar and Singapore dollar were also supported by speculation about a possible rise in the Chinese currency ahead of US President George W. Bush's visit to China that starts on November 19.
President Bush, who will visit Beijing as part of a four-nation trip to Asia, urged China on Tuesday to do more to allow the yuan to strengthen and said the trade imbalance between the two countries was "bothersome".
Bush told Asian journalists he planned to discuss his hopes for more currency flexibility with Chinese President Hu Jintao.
The comments failed to push up the yuan in non-deliverable forward contracts, which investors use to bet on the Chinese currency. But analysts said Asian currencies are likely be supported as pressure on China mounts ahead of Bush's trip.
Asian currencies could get a boost if the Chinese yuan is allowed to rise, because the region's authorities increasingly benchmark their currencies against the yuan to enable their exporters to stay competitive against China.
"Whenever you have such events, there's always more caution - people are less willing to go long on the greenback," said Thomas Lam, treasury economist at United Overseas Bank.
Still, Lam does not expect any big move from China in the coming year because of growing global economic uncertainties, an expected slowdown in China's economy and on China's reluctance to succumb to external political pressure.
He expects the yuan to rise by just 1 percent by the end of 2006 following a 0.3 percent rise since July 21, when China revalued the currency by 2.1 percent to 8.11 per dollar.
UBS said in a report although the currency markets would watch Bush's China trip closely, "we expect the Chinese will not move further on the yuan in the near term.