The Malaysian ringgit slid on its weakness in non-deliverable forwards. The Indonesian rupiah edged weaker on dollar-demand from local importers for month-end payments.
South Korea's won eased as investors covered short positions in the dollar with daily spot dollar/won trading volume at lowest so far this year.
The dollar stayed firm against a basket of six major currencies after US data showing new claims for benefits stayed around their pre-recession levels last week and manufacturing in the Mid-Atlantic region accelerated in April.
Asian shares edged lower amid sustained tensions in Ukraine. At least three people were killed in a gunfight in the early hours of Sunday near a Ukrainian city controlled by pro-Russian separatists.