President Xi Jinping has told his US counterpart Joe Biden that the world is big enough for both China and the United States to prosper, and stressed that differences between the two countries should not be an obstacle to growing relations.

The two met on the Indonesian island of Bali on Monday for their first face-to-face discussion since Biden took office almost two years ago.

There were smiles and handshakes as the two presidents met ahead of the start of the G-20 summit on Tuesday, and both leaders stressed the need to boost ties and find areas for cooperation.

After the pleasantries, the pair spoke behind closed doors for more than three hours.

Following the meeting, the Foreign Ministry said Xi had told his US counterpart that the world was "big enough" for their two countries to prosper and that they shared "more, not less" interests.

State media reported that Xi stressed that the Taiwan question is at the very core of China's interests, is the bedrock of the political foundation of Sino-US relations, and is the first red line that must not be crossed.

The president also told his US counterpart that the so-called "democracy versus authoritarianism" narrative is not the defining feature of today's world. Xi said freedom, democracy and human rights are the common pursuit of humanity.

He said China took great pride in its own style of democracy, based on the country's reality, history and culture, and that it reflects people's will. The President told Biden that differences between the two countries should not get in the way of Sino-US relations.

Speaking after the meeting, Biden said that Washington's "One China" policy had not altered and it opposed any unilateral change in the status quo by either side.

"It was also clear that China and the United States should be able to work together where we can, to solve global challenges that require every nation to do its part," Biden told reporters.

"We discussed Russia's aggression against Ukraine, reaffirmed our shared belief in the threat, or the use of nuclear weapons is totally unacceptable and I ask that [US Secretary of State] Antony Blinken travel to China to follow up on our discussions and keep the line of communication open between our two countries."

He added: "I absolutely believe there need not be a new cold war. I've met many times with Xi Jinping and we were candid and clear with each other across the board."

The US President said he was convinced that both he and Xi understood exactly what the other side was saying.