Most Southeast Asian stock markets rose on Monday, mirroring gains in Asian peers, except Vietnam, which fell for a second straight session after its government cut the gross domestic product growth target for 2016.

In Asia, a report that Deutsche Bank was negotiating a much smaller fine with the U.S. Department of Justice pushed shares higher, with MSCI's broadest index of Asia-Pacific shares outside Japan edging up 0.8 percent.

Sentiment got a boost after oil prices stabilised on hopes that the OPEC output cut would help re-balance markets.

Indonesia outperformed regional markets, and climbed nearly 2 percent, supported by gains in consumer non-cyclicals and energy stocks.

The country's annual inflation rate in September edged up from that in August, but remained close to a near seven-year low, data from the statistics bureau showed on Monday.

"We are seeing some positive sentiment because Jokowi (Indonesian President Joko Widodo) has asked for a higher budget in terms of capex in 2017," said Harry Su, an analyst with Jakarta-based Bahana Securities.

"If this comes through then obviously the spending would increase, which in turn, could be positive for GDP growth."

The Jakarta Post reported on Saturday that the Indonesian government planned to improve the quality of spending after recent budget cuts.  

Singapore stocks finished flat, after hitting its highest in more than three weeks earlier in the day.

Philippine shares bounced back from Friday's losses to post a gain of 0.6 percent, pulled up by industrials and consumer non-cyclical stocks.

Thai shares were buoyed by gains in energy stocks. While PTT PCL rose 2.4 percent, Thai Oil PCL notched up 1.8 percent.

Thailand's consumer prices rose for a sixth straight month in September, but the pace remained benign, commerce ministry data showed on Monday.

Bucking the trend, Vietnam shares posted a one-week closing low after the government slashed annual GDP growth target to between 6.3 percent and 6.5 percent due to a slowing economy. Initially, the government had targeted a GDP growth of 6.7 percent for this year.

The Malaysian stock market was closed for a holiday.