Woodside, California. US President Joe Biden and China’s Xi Jinping emerged Wednesday from their first face-to-face meeting in a year vowing to stabilize their fraught relationship and showcasing modest agreements to combat illegal fentanyl and re-establish military communications. But there were still deep differences in economic competition and global security threats.

The most assuring takeaway from the meeting for Biden was that if either man had a concern, “we should pick up the phone and call one another and we'll take the call. That's important progress," he said in a news conference following the talks.

The two leaders spent four hours together at a bucolic Northern California estate -- in meetings, a working lunch and a garden stroll -- intent on showing the world that while they are global economic competitors they’re not locked in a winner-take-all faceoff.

“Planet Earth is big enough for the two countries to succeed,” Xi told Biden.

The US president told Xi: “I think it’s paramount that you and I understand each other clearly, leader-to-leader, with no misconceptions or miscommunications. We have to ensure competition does not veer into conflict.”

Their meeting, on the sidelines of the annual Asia-Pacific Economic Cooperation conference, has far-reaching implications for a world grappling with economic cross-currents, conflicts in the Middle East and Europe, tensions in Taiwan and more

They reached expected agreements to curb illicit fentanyl production and to reopen military ties, Biden said. Many of the chemicals used to make synthetic fentanyl come from China to cartels that traffic the powerful narcotic into the US, which is facing an overdose crisis.

Top military leaders will resume talks, Biden said, an increasingly important move particularly as unsafe or unprofessional incidents between the two nations’ ships and aircraft have spiked.

Ultimately, the agreements rely on trust between the two leaders.

“I know the man I know his modus operandi,” Biden said of Xi. “We have disagreements but he’s been straight.”

But he still said Xi was a dictator ... “in a sense.”

The two leaders had a significant back and forth over Taiwan, with Biden chiding China over its massive military build-up around Taiwan and Xi telling Biden he had no plans to invade the island, according to a US official who spoke on condition of anonymity to detail the private talks.

Biden, the official said, declared the US was committed to continuing to help Taiwan defend itself and maintain deterrence against a potential Chinese attack, and also called on China to avoid meddling in the island’s elections next year. The official described the Taiwan portion of the talks as “clear-headed” and “not heated.”

Biden also called on Xi to use his influence with Iran to make clear that Tehran, and its proxies, should not take steps that would lead to an expansion of the Israel-Hamas war. Foreign Minister Wang Yi has assured the US that the Chinese have communicated concerns to Iran on the matter. But the official said the US has not been able to ascertain how seriously the Iranians are taking concerns raised by Beijing.

According to a statement released by China Central Television, the state broadcaster, Xi was most focused on Taiwan and the US sanctions and restrictions against Chinese products and businesses.

Xi urged the US to support China’s peaceful unification with the self-governed island, calling Taiwan "the most important and most sensitive issue” in the bilateral relations. He also raised Beijing’s concerns over export controls, investment screenings, and sanctions imposed by the US, which he said “have severely harmed China’s legitimate interests."

He said, “We hope the US side can seriously treat China’s concerns and take actions to remove unilateral sanctions and provide a fair, just, non-discriminatory environment for Chinese businesses.”

Xi said he and Biden also agreed to establish dialogues on artificial intelligence and stressed the urgency for the two countries to cope with the climate crisis, the state broadcaster reported.

Both leaders acknowledged the importance of their relationship and the need for better coordination. But their differences shone through: Xi indicated he wants better cooperation -- but on China's terms. And he sought to project strength to his domestic audience in the face of US policies restricting imports from China and limiting technology transfers to Beijing.

Biden, meanwhile, will also spend time this week in California working to highlight new alliances in the Indo Pacific and efforts to boost trade with other regional leaders.

They sought to build back to a stable baseline after already tense relations took a nosedive following the US downing of a Chinese spy balloon that had traversed the continental US, and amid differences over the self-ruled island of Taiwan, China’s hacking of a Biden official’s emails and other matters.

For Biden, Wednesday's meeting was a chance for the president to do what he believes he does best: in-person diplomacy.

“As always, there's no substitute for face-to-face discussions,” he told Xi. With his characteristic optimism, Biden sketched a vision of leaders who manage competition “responsibly,” adding, "that's what the United States wants and what we intend to do.”

Xi, for his part, was gloomy about the state of the post-pandemic global economy. China’s economy remains in the doldrums, with prices falling due to slack demand from consumers and businesses.

“The global economy is recovering, but its momentum remains sluggish,” Xi said. “Industrial and supply chains are still under the threat of interruption and protectionism is rising. All these are grave problems."

Biden and Xi held their talks at Filoli Estate, a country house and museum about 25 miles (40 kilometers) south of San Francisco. The event was carefully staged, Biden first to arrive at the grand estate.

After a handshake and smiles, the presidents and their respective aides on trade, the economy, national security and regional diplomacy gathered across from one another at a single long table, the culmination of negotiations between the two leaders’ top aides over the past several months. It was Biden and Xi’s first conversation of any kind since they met last November in Bali.

Next came a working lunch with inner-circle members from both administrations. They ate ravioli, chicken and broccolini, with almond meringue cake and praline buttercream for dessert.

Before they parted, the two strolled the property along a red brick path through impressive topiary and knotted gothic trees. Asked by reporters how the meeting went, the president said “well” and flashed a thumbs up.

There were light moments between the two leaders who have logged much time together over the last decade. Biden asked Xi to extend his early birthday wishes to Xi’s wife, who will be celebrating next week. Xi thanked the president for reminding him. The Chinese leader said that he’s been so busy working he had forgotten the big day was nearing.

The relationship between China and the US has never been smooth, Xi said. Still, it has kept moving forward. "For two large countries like China and the United States, turning their back on each other is not an option,” he said.

More pointedly, Xi also suggested it was not up to the US to dictate how the Chinese manage their affairs, saying, “It is unrealistic for one side to remodel the other, and conflict and confrontation has unbearable consequences for both sides.”