President Biden and China's President Xi Jinping shake hands as they begin talks in Bali.

NUSA DUA, Indonesia — President Biden and Chinese leader Xi Jinping took a small but significant step toward stabilizing what has become an increasingly fraught relationship when they met for over three hours of talks on Monday.

The two leaders "were very blunt with one another" on a range of topics where they do not see eye to eye, Biden told reporters after the meeting. But he said the they had agreed to further discussions among key officials, and to a visit to China by Secretary of State Antony Blinken, set to take place sometime early next year.

Chinese foreign ministry spokeswoman Hua Chunying, who was in the meeting, said on Twitter the two leaders "instructed their teams to promptly follow up and implement common understandings reached between them, and take concrete actions to put China-U.S. relations back on the track of steady development."

While Biden and Xi have met several times over the years, this was their first face-to-face meeting since Biden became president. Both leaders had expressed hope ahead that the long-awaited in-person meeting would help stabilized the relationship, which has seen trust evaporate and disputes fester across a range of issues, from trade and technology to Taiwan.

Biden said he believe that "there need not be a new Cold War" between the U.S. and China. According to a read-out from China's state news agency, Xi appeared to agree, saying "China-U.S. relations should not be a zero-sum game where you lose and I win, and you rise and I fall."

Despite agreeing to hold further discussions, a good portion of the meeting appeared to be a series of exchanges of viewpoints on areas where the two disagree.

On Taiwan, Biden reassured Xi that U.S. policy has not changed, and that the United States does not support changes to the status quo from either side.

"I'm convinced that he understood exactly what I was saying. I understood what he was saying," Biden told reporters.

Beijing considers Taiwan a part of China, and hopes to unite the island politically with the mainland. Xi has said he hopes to do so peacefully, but Beijing cannot rule out the possible use of force.

Biden told reporters he did not believe there would be any imminent attempt by China to invade Taiwan.

Xi told Biden the Taiwan issue was "the number one un-crossable red line" in China-U.S. relations. He said it's an issue for the people of China to resolve, and he hoped the U.S. would live up to its commitments and words.

On North Korea, which has been testing ballistic missiles and may be preparing for a fresh nuclear test, Biden said he was unsure if China was able to control Pyongyang. But he thought Beijing had an obligation to attempt to dissuade North Korea.

If they do conduct a test, Biden said he told Xi the U.S. would "do what we need" to defend itself and its allies — and that could mean "we'd be more up in the face of China." Administration officials have said the U.S. could respond to more provocations from North Korea by boosting the U.S. military presence in the region.

Biden said that the midterm elections had sent a message around the world that the U.S. would remain fully engaged in global affairs. Xi, for his part, cemented his power last month when he got a third term as head of the ruling Communist Party and was able to stack the leadership with allies and loyalists.

Biden said he found Xi neither more confrontational nor conciliatory than in the past. And he added: "Do I think he's willing to compromise on various issuse? Yes."

But he struck a cautious tone about the road ahead.

"We're not going to be able to work everything out. I'm not suggesting this is kumbaya," Biden said.

The White House listed global issues like climate, debt relief, health security and food security as areas in which the two leaders "agreed to empower key senior officials to maintain communication and deepen constructive efforts."

The White House said Biden and Xi both "reiterated their agreement that a nuclear war should never be fought and can never be won and underscored their opposition to the use or threat of use of nuclear weapons in Ukraine."

Heading into the meeting, Biden had reiterated his call to responsibly manage the emerging competition between the two sides.

"As the leaders of our two nations, we share responsibility in my view to show that China and the U.S. can a mange our differences, prevent competition from becoming anything nearing conflict and to find ways to work together on urgent, global issues that require our mutual cooperation," Biden said to Xi at the start of the meeting.

Xi told Biden that the bilateral relationship currently "is not what the international community expects" and said the leaders need to "elevate the relationship."