Market sentiment was buoyed after U.S. President Donald Trump said he had a "very good call with his Chinese counterpart Xi Jinping on Saturday and claimed "big progress" was being made on trade discussions.

Regional currencies came under pressure from multiple factors in 2018 including the Sino-U.S. trade conflict, the U.S. Federal Reserve's hawkishness, and worries over global economic slowdown.

Mizuho Bank in a note to clients said that despite valuation in emerging market assets becoming increasingly attractive, investors remain cautious as some see potential risks ahead.

The Indonesian rupiah strengthened as much as 0.8 percent on Monday but pared some gains by 0400 GMT.

However, the rupiah was poised to weaken over 6 percent this year, after it breached the 15,000 per dollar mark in October, a level last seen in the Asian financial crisis two decades ago.

The Malaysian rinngit gained 0.3 percent against the greenback, while the Singapore dollar was marginally firmer.

Meanwhile, the Indian rupee strengthened 0.2 percent on the last trading day of the year, but remained the worst performing currency in the region.

The rupee weakened this year on concerns of a widening current account deficit as rising global crude oil prices increased to cost of imported fuel. Though the rupee regained some ground as the strength in oil prices faded, investors remain concerned ahead of a general election due by May, as Prime Minister Narendra Modi's market-friendly party fared poorly in regional polls in earlier this month.

The Taiwan dollar, the Korean won, the Thai baht and the Chinese yuan were not trading on account of holidays.

The following table shows rates for Asian currencies against the dollar at 0400 GMT.