The Taiwan dollar dropped as far as T$33.8 per US dollar and the Korean won fell to a 2005 low around 1,062 per US dollar before recovering to close local trade around 1,058.
Thailand's markets were closed for a holiday.
Other Southeast Asian currencies such as the Singapore dollar and Philippines peso shed about a quarter of a percent each against the US currency in early dealing, before reclaiming some lost ground.
"The dollar has gained some momentum but much will depend on what happens to dollar/yen," Jan Lambregts, head of Asia-Pacific research at Rabobank, said.
He said that technically the yen's decline to the weaker side of 115 a dollar raised the possibility of it falling further, even beyond 120.
But economic fundamentals, equity inflows into Japan and expectations for further gains in the Chinese yuan argued for longer-term yen strength, he said.
Lambregts said that would propel Asian currencies higher longer term, even though he expected only a modest half-a-percent rise in the yuan by the end of the year.
Analysts said the US dollar was being propped up by strong inflation and economic data from the United States this month, and a wave of hawkish comments from Federal Reserve officials.
US companies taking advantage of the Homeland Investment Act (HIA), giving tax breaks to foreign revenue brought back to the United States during 2005 were also supporting the dollar.
"We do believe the US dollar will eventually come lower on the back of a lack of financability of the imbalances in the US external sector," UBS analysts wrote in a note to clients.
There had been few reasons to buy Asian currencies in the last three months and it was pointless trying to bet against the dollar's ascent, they said.
"There may not be good reason to fight its ascent at a time when it's being supported by HIA flows, an aggressive Fed, and reasonably strong economic data, although we are watching closely the degree of response of the US dollar to talk of higher interest rates," UBS said.
Moreover, Asian currencies were highly sensitive to equity markets, which continued to see outflows of foreign investment, they said.
Data from Taiwan's stock exchange showed foreigners have been heavy net sellers for nine sessions, and had sold stocks worth over $1.2 billion during that period.