Japan's Nikkei 225 index was up close to 2% in morning trade, led by the tech sector.

The US last week announced proposed tariffs against China, which sent US and Asian markets tumbling.

But China's premier Li Keqiang said on Monday that China and the US should maintain negotiations.

Mr Li's comments followed those made earlier by US Treasury secretary Steven Mnuchin, who told US media on Sunday he was "cautiously hopeful" that the US and China could come to an agreement on trade issues.

On Wall Street, the S&P 500 finished Monday's session up 2.7%, the Dow Jones gained 2.8%, and the tech-heavy Nasdaq Composite ended up 3.3%.

By the lunch break on Tuesday, the Nikkei 225 index was up 1.7% to 21,110.68, with tech shares, which would be hurt in an ongoing trade war, keeping the index in positive territory.

Tokyo-listed stocks in the semiconductor equipment maker Tokyo Electron were up 2.4%, while shares in robot maker Yaskawa Electric Corp were up 2.25%.

Elsewhere in Asia, South Korea's benchmark Kospi index was up 0.5% to 2,449.4 points, and Australia's S&P/ASX 200 index was up 0.7% to 5,828.4.

In China, Hong Kong's Hang Seng index added 0.8% to 30,80 points, while the Shanghai Composite had gained 1% in mid-morning trade to 30,794.36.

Tariff talk
US President Donald Trump announced the tariffs against Chinese goods on Thursday, saying they were a response to allegations of intellectual property theft by China.

China then responded to news of the planned tariffs by saying it did not want a trade war, but it was "absolutely not afraid" of one.

Some analysts have said if a full blown trade war is not averted, China could make things difficult for US companies doing business in China, among other measures, while others have said China is more likely to try and avoid escalating the problem.

In response to US tariffs on steel and aluminium imports announced by Mr Trump earlier this month, China has already announced its own set of proposed tariffs worth $3bn.

The US tariffs on steel and aluminium imports came into effect last week.