Trading was subdued with offshore interest subdued as US and British financial markets are closed on Monday.
The Indonesian rupiah rose on bond inflows and the Malaysian ringgit gained on daily-fixing demand.
Taiwan's dollar advanced as local stocks hit their highest closing level in nearly three years on foreign demand.
The South Korean won ended local trade firmer on month-end demand from exporters, while caution over possible intervention by the foreign exchange authorities limited its upside.
Dollar/won spot trading volume in the domestic market fell to $2.8 billion, the lowest since November 2008, according to currency brokers.
Asian stocks rose on a strong Wall Street and a decisive win for billionaire Petro Poroshenko in Ukraine's presidential election.