Offshore funds and domestic exporters lifted the won by 0.5 percent against the dollar.
The South Korean currency also hit its strongest in more than 15 months versus the yen amid expectations that next month's election in Japan will result in victory for an opposition, the Liberal Democratic Party, that wants the central bank to aggressively ease monetary policy.
The Taiwan dollar gained on inflows from foreign financial institutions and demand from exporters. Interbank speculators increased long positions in the Malaysian ringgit and the Philippine peso rose on remittance inflows.
Regional stocks advanced after US Republican and Democratic congressional leaders emerged from a meeting with President Barack Obama on Friday pledging to find common ground on taxes and spending that would allow them to avert a "fiscal cliff" that could send the economy back into recession.
"Optimistic news on the fiscal cliff could resume an appreciation trend in emerging Asian currencies," said Jeong My-young, research head of Samsung Futures in Seoul.
"Still, we have not seen a resolution yet. The negotiations are ongoing and there would be ups and down, given characters of politics," Jeong added.
Last week, most emerging Asian currencies slid as investors shed riskier assets on worries over the US fiscal problems.
Investors are concerned over whether European officials meeting on Tuesday to discuss aid for debt-ridden Greece can reach agreement on Friday.
Dealers are also wary of possible intervention by Asian central banks to stem their currencies' gains amid all the uncertainties afflicting other regions.
WON
The won rose on demand from offshore leveraged funds and local exporters, dealers said.
The South Korean currency hit 13.3260 per yen, its strongest since Aug. 4, 2011.
The won is likely to stay firm despite caution over dollar purchases by the foreign exchange authorities to stem its strength, they added.
"The won will not fall without strong intervention. Exporters will keep selling dollars by month-end," said a senior foreign bank dealer in Seoul.
Still, some analysts and dealers saw risks of corrections as investors may book profits on a won that is the second best performer this year among emerging Asian currencies, with a 6.0 percent gain against the dollar.
Barclays expected profit taking concern over potential intervention to weaken the won before a presidential election in December.
Barclays advised selling the won against the ringgit with a one-month target of 375.0. The ringgit eased 0.2 percent to 354.6.
"We think that Bank Negara Malaysia will allow a degree of MYR outperformance versus its trading partners' currencies after marked underperformance in Q3, particularly versus the KRW," it said in a note.
RINGGIT
The ringgit gained as interbank speculators cut dollar holdings, tracking a firm Singapore dollar.
But some investors hesitated to add more bullish bets on the Malaysian currency, given uncertainty over the US fiscal cliff.
"It is too early to say we want to short dollar/ringgit here. The US negotiation can go either way again and risk assets appeared to be a bit oversold," said a Malaysian bank dealer in Kuala Lumpur.
TAIWAN DOLLAR
The Taiwan dollar advanced on exporters' demand for settlements and inflows from foreign financial institutions.
Exporters aggressively bought the Taiwan dollar when it was weaker than 29.180 to the US dollar, dealers said.
But some foreign financial investors unloaded the island's currency amid caution over potential intervention by the central bank to stem its appreciation, they added.
PHILIPPINE PESO
The Philippine peso rose on remittance inflows and as interbank speculators resumed building bullish positions in the peso. Dollar-short covering last week gave investors with chances to buy the peso on dips, dealers said. The Philippine currency lost 0.7 percent against the dollar last week, according to Thomson Reuters data.
Still, investors stayed wary of potential intervention by the central bank to keep the peso weaker than 41.20 to the dollar.
"As long as positive news keeps coming from the US, dollar/peso will remain on track to test 41.00 before year ends," said a foreign bank dealer in Manila.
SINGAPORE DOLLAR
Offshore funds, custodian banks and local interbank speculators lifted the Singapore dollar, dealers said.
Some investors reduced long positions in the US dollar as the greenback failed to stay stronger than 1.2300 to the Singapore dollar.