Mainland Chinese shares were the biggest gainers in Asia on Monday, a day which also saw the other major stock markets in the region advance, with trade talks between the U.S. and China set to continue in Washington this week after high-level meetings in Beijing concluded last week.

The Shanghai composite jumped around 2.68 percent to close at about 2,754.36 while the Shenzhen component rose 3.954 percent to finish at approximately 8,446.92. The Shenzhen composite advanced 3.705 percent to close at around 1,440.95.

Hong Kong's Hang Seng index also gained about 1.5 percent, as of its final hour of trading.

Japan's Nikkei 225 jumped 1.82 percent to close at 21,281.85, while the Topix also advanced 1.56 percent to finish its trading day at 1,601.96. Shares of Fast Retailing, the company behind the Uniqlo chain of apparel stores, surged 3.9 percent.

Meanwhile, the Kospi in South Korea gained 0.67 percent to close at 2,210.89 as industry heavyweight Samsung Electronics saw its shares rise 0.33 percent.

Australia's rose 0.39 percent to close at 6,089.80 as most sectors saw gains. The energy subindex rose 1.57 percent as shares of the oil companies advanced. Santos traded 1.19 percent higher, Woodside Petroleum gained 2.3 percent and Beach Energy advanced 3.18 percent.

Earlier on Monday, the Australian government announced that the national parliament's computer network had been hit by an attack in February. Prime Minister Scott Morrison told parliament that "cyber experts believe that a sophisticated state actor is responsible for this malicious activity."

Over in Singapore, DBS gained 1.86 percent in afternoon trade after the bank announced a 28 percent increase in net profit in 2018.

Despite Monday's gains, one strategist warned that the markets are "risky" at the moment.

"Look at how weak markets were on Friday, look how strong they are today. They're very volatile and this volatility that we're seeing on a day-to-day basis is actually, you know, a sign that people are not that sure what's ... going on," Mark Jolley, global strategist at CCB International Securities, told CNBC's "Street Signs."