Japan's Nikkei 225 (N225) rose 0.5%. The market also got a boost after Japan revised its gross domestic product growth to an annualized 1.8% for the third quarter, compared with the initial estimate of 0.2%.
South Korea's Kospi (KOSPI) also gained 0.3%.
Hong Kong's Hang Seng (HSI) opened slightly higher, but then bounced between small gains and losses. The benchmark was last up 0.3%.
China's Shanghai Composite (SHCOMP) also seesawed and briefly slipped 0.2%. It then reversed losses and traded flat.
Jingyi Pan, a market strategist for IG Group, said traders are closely watching to see whether US and Chinese negotiators can strike a trade deal before December 15, when a new round of American tariffs are set to take effect on around $160 billion worth of Chinese goods,
The latest Chinese trade data also suggests it's more urgent for Beijing to ink a deal with Washington in order to ease economic pressure, she added.
China's exports dropped by a worse-than-expected 1.1% in November from a year prior, marking a fourth straight month of decline, according to government data released on Sunday. That was mainly because shipments to the United States plunged 23%, as the long-running trade war continues to hurt Chinese exporters.
Imports rose 0.3% from a year earlier — the first increase since April.
CNN's Junko Ogura in Tokyo contributed to the report.