Southeast Asian stock markets rose on Tuesday, with Vietnam scaling an all-time peak, as reports of U.S.-China trade negotiations and the Chinese premier's pledge to ease access for U.S. businesses eased fears of a trade war.

Chinese Premier Li Keqiang on Monday said China would treat foreign and domestic firms equally, would not force foreign firms to transfer technology and would strengthen intellectual property rights.

Li's pledge followed a Wall Street Journal report that said Washington asked Beijing in a letter last week to cut a tariff on U.S. autos, buy more U.S. made semiconductors and give U.S. firms greater access to the Chinese financial sector.

U.S. Treasury Secretary Steven Mnuchin and Trade Representative Robert Lighthizer listed steps they want China to take in a letter to Liu He, a newly appointed vice premier who oversees China's economy, the Journal said, quoting sources with knowledge of the matter.

Asian shares climbed, with MSCI's broadest index of Asia-Pacific shares outside Japan rising over 1 percent, its second gain in five sessions.

Indonesian shares rose 0.6 percent after three straight sessions of losses, with financials driving the benchmark.

The index of the country's 45 most liquid stocks rose 0.6 percent.

"Composition of financials in Indonesia is about 29 percent of the total market cap. Think most likely investors look at financials as the first to sell when market is turbulent, but are also the first to be bought when there is any kind of rebound in the market," Taye Shim, head of research at Mirae Asset Sekuritas.

Bank Central Asia Tbk was the top contributor to the index, rising as much as 2.2 percent.

Vietnam shares surged as much as 1.4 percent, buoyed by financials.

Joint Stock Commercial Bank for Investment and Development of Vietnam was the biggest boost to the benchmark, rising as much as 3.8 percent to hit a record.

Singapore Shares rose 0.5 percent and was set to break a four-session losing run. 

Financials led the charge, with DBS Group Holdings rising as much as 1.5 percent, its first rise in four sessions.

Philippine shares rose 0.3 percent, buoyed mainly by financials and real estate stocks.

Ayala Land rose 1.4 percent and was the top boost to the index.

Thai shares rose 0.3 percent, boosted by financials.

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