- Elsewhere, the Taiwanese dollar strengthened and equities rose after the island nation's central bank said it may hike its annual growth forecast.
Indonesian stocks eased on Monday ahead of a central bank meeting the following day, while a surge in coronavirus cases pushed Indian shares down nearly 3% in early trade.
Currency moves in Asia were muted on Monday amid a lack of major catalysts and ahead of a slew of economic data from across the region this week.
Thai, Taiwanese and Singapore shares gained, while those in Malaysia and the Philippines edged lower.
Fresh waves of COVID-19 infections in South and Southeast Asia have sapped risk appetite in recent days, while recent weakness in currencies like the Russian rouble and the Turkish lira has weighed more broadly on emerging markets.
Indonesia's stocks and the rupiah will be in focus early this week as Bank Indonesia (BI) reviews its policy settings to support economic recovery and maintain stability in financial markets.
Analysts expect BI to leave its key policy rate unchanged at a record low for the rest of the year, according to a Reuters poll. The bank has held rates steady in recent times to support the rupiah amid global market uncertainty.
Though BI maintains the currency is "stable" compared with its emerging market peers, it has already depreciated 3.5% against the US dollar this year and is among Southeast Asia's worst performers.
"Since currency stability is BI's key mandate, further policy rate cuts look unlikely this year, especially given that the economy is also showing a cyclical recovery," Morgan Stanley analysts said in a note.
Indonesia has also struggled to sell its bonds as signs of a robust economic recovery in the United States has driven US Treasury yields higher and moved capital away from one of the highest-yielding debt instruments in emerging markets.
Yields on the US 10-year benchmark eased last week as markets bought into the US Federal Reserve's accommodative policy stance, but Morgan Stanley analysts believe the outlook for Indonesian bonds remains tough.
"Demand at INDOGB auctions has still been weak, and we think that, looking ahead, external factors such as US yields will likely remain uncertain," they said.
"While the rates differentials between Indonesia and the US are still wide, without BI hiking rates, the bonds and IDR would still face sell-off pressure."
Elsewhere, the Taiwanese dollar strengthened and equities rose after the island nation's central bank said it may hike its annual growth forecast.
In Thailand, stocks gained nearly 1%, even as the tourism-reliant nation reported another record rise in virus cases on Sunday.
India reported a record rise in coronavirus infections of 273,810 on Monday, taking its overall case load past 15 million, second only to the United States globally.