Stock markets in Thailand and Vietnam edged up on Monday, in line with broader Asia, but trading was thin as all the other markets in Southeast Asia were closed for the religious holiday of Eid al Fitr.

MSCI's broadest index of Asia-Pacific shares outside Japan ticked up 0.4 percent.

Oil prices rose more than 1 percent on a weaker dollar, but another rise in U.S. drilling activity stoked worries that a global supply glut will persist despite an OPEC-led effort to curb output.

Vietnam rose 0.4 percent to hit a fresh nine-year high, led by gains in financials, real estate and energy stocks.

Vingroup JSC climbed 1.3 percent, while Vietnam National Petroleum Group gained 1 percent.

"We observe that the money flow in the stock market is quite strong at the moment," said Tran Minh Hoang, chief economist of Vietcombank Securities.

Thai shares climbed 0.4 percent to touch a more than two-month high, with Bangkok Dusit Medical Services  and U City rising 1.6 percent and 33.3 percent, respectively.

Financial markets in Singapore, Malaysia, Indonesia and the Philippines were closed on Monday for the Islamic holiday of Eid al Fitr, marking the end of the holy month of Ramadan.