Bali, Indonesia - US President Joe Biden and his Chinese counterpart, Xi Jinping, spoke for some three hours during their eagerly-awaited meeting in Indonesia, which covered everything from Taiwan to environmental action.

On Monday, the two leaders had their first face-to-face meeting since Biden took office almost two years ago. They greeted each other with a handshake and went on to discuss a wide range of issues that have brought relations between the US and China to an all-time low.

Overall, the meeting, held ahead of the G20 summit hosted by Indonesia, was a mixed bag, leading to some encouraging signs of possible collaboration while also highlighting areas of major disagreement.

"Climate change, global macroeconomic stability including debt relief, health security, and global food security" were name-checked by the official White House readout as global priorities, on which Biden insisted the two countries had to work together.

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Both presidents had instructed their top officials to "maintain communication and deepen constructive efforts on these and other issues," the statement added.

However, the hoped-for formal resumption of official climate dialogue, which China had broken off in August amid tensions with the US over Taiwan, was not announced. And these tensions are set to continue, based on Xi's remarks during the talks.

The Chinese leader made it clear that he wants the US to stay out of the conflict over Taiwan.

"Resolving the Taiwan question is a matter for the Chinese and China's internal affair," Xi said, according to Chinese sources. He added that it was "the first red line that must not be crossed in China-US relations."

"National reunification" was underlined as a "common aspiration" of the Chinese people.

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"Anyone that seeks to split Taiwan from China will be violating the fundamental interests of the Chinese nation; the Chinese people will absolutely not let that happen," Xi reportedly warned. Biden has previously said that the US will defend the island militarily in case of an invasion, although on Monday he insisted that there was no evidence of any such attack.

There were also complaints over the trade war between the two superpowers, which the Chinese leader blamed on the US.

"Starting a trade war or a technology war, building walls and barriers, and pushing for decoupling and severing supply chains run counter to the principles of market economy and undermine international trade rules," Xi said.

He is also said to have told Biden: "It is in our mutual and fundamental interest to prevent conflict and confrontation and achieve peaceful coexistence."

That was an encouraging note echoed by Biden, who said in remarks after the meeting: "I absolutely believe there's not been a new Cold War."

Both he and Xi had also agreed that the use or threat of nuclear weapons should be avoided. This applied in particular Russia's war in Ukraine, over which China's president said he was "highly concerned." However, Xi again stopped short of condemning the invasion and only encouraged dialog.