Stocks in Asia Pacific were mixed on Monday, while oil prices continued to rise as tensions between the U.S. and Iran lingered after the latter shot down an American surveillance drone.

Mainland Chinese stocks were mixed on the day, with the Shanghai composite up 0.21% to 3,008.15, while the Shenzhen component was largely flat at 9,212.12 and the Shenzhen composite fractionally lower at 1,576.09.

Over in Hong Kong, the Hang Seng index was about 0.1% higher, as of its final hour of trading.

Japan's Nikkei 225 finished its trading day 0.13% higher at 21,285.99, while the Topix index gained 0.12% to close at 1,547.74.

In South Korea, the Kospi closed largely unchanged at 2,126.33.

Australia's rose 0.22% to close at 6,665.40. The country's central bank governor Philip Lowe said on Monday it would be legitimate to question the effectiveness of global monetary policy easing to boost economic growth even as the country itself is on a path to further lower domestic interest rates.

In the minutes of its June monetary policy meeting, the Reserve Bank of Australia had said it was "more likely than not" that further easing would be "appropriate," following a decision to lower the cash rate by 25 basis points to 1.25%.

The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 96.142 after slipping from levels above 97.5 last week.

The traded at 107.41 against the dollar after touching levels above 108.5 in the previous trading week. The changed hands at $0.6950 after rising from levels below $0.684 last week.

Meanwhile, a highly-anticipated meeting between Chinese President Xi Jinping and U.S. President Donald Trump is set to happen later this week at the G-20 summit in Japan as the two economic powerhouses seek to find a resolution to their protracted trade fight.

"I really cannot remember a G-20 as important as this, maybe with the exception of those that took place during the global financial crisis," Stefan Hofer, managing director and chief investment strategist at LGT Bank Asia, told CNBC on Monday.