Beijing. Presidents Donald Trump and Xi Jinping wrapped up critical talks on Friday, claiming important progress in stabilizing US-China relations even as big differences persist between the world’s two biggest powers on Iran, Taiwan, and more.

Xi welcomed Trump at his official residence, Zhongnanhai, on Friday for the final talks of the summit before the US leader’s return to Washington. The leaders took a short walk through the grounds that feature ancient trees and Chinese roses, and strolled through a covered passageway with green columns and archways painted with birds and traditional Chinese mountain scenes.

Over tea and lunch, Trump and Xi -- with top aides and translators in tow -- huddled for nearly three hours of talks before the US leader completed his three-day visit to China.

“It’s been really a great couple of days,” Trump told reporters as he sat with Xi before the start of their meeting with aides.

Xi, for his part, called it a “milestone” visit. “We have established a new bilateral relationship, or rather a constructive, strategic, stable relationship,” he said.

But the optimistic outlook collides with some difficult truths about the thorniest issues between the two superpowers.

Beijing has shown little public interest in US entreaties to get more involved in solving the conflict in Iran, even though Trump said in an interview with Fox News' Sean Hannity that in their conversations, Xi had offered to help.

In recent weeks, the US State Department has accused Chinese firms of providing satellite imagery to the Iranian government, and the Treasury Department has moved to target Chinese oil refineries accused of buying oil from Tehran, as well as shippers of the oil.

And the White House believes China can still do more to stem the flow of Chinese-made precursor chemicals into Mexico, used to make illicit fentanyl that has wreaked havoc on many US communities.

Xi, meanwhile, warned Trump during private talks that their differences on the self-ruled island of Taiwan, if handled poorly, could hurtle the world's dominant powers toward “clashes and even conflicts,” according to Chinese government officials.

Trump appeared impressed by the bucolic grounds, remarking that the roses were the most beautiful he had ever seen. Xi promised to send him some rose seeds.

The compound is wrapped around two manmade lakes that had been built for the pleasure of emperors. Zhongnanhai is often compared to the White House, the Kremlin or South Korea’s Blue House. But unlike the other presidential residences, Zhongnanhai does not serve as the main venue for diplomatic visits. The invitation appeared to be an attempt by Xi to extend a personal touch to a US leader who appreciates big gestures.

“I think he’s a warm person, actually. But he’s all business,” Trump said of Xi in the Fox News interview. “There’s no games.”

China Wants the Strait of Hormuz Opened
The leaders agreed that the Strait of Hormuz -- effectively closed since the start of the Iran conflict -- needs to be reopened to support global energy demands. About 20% of the world’s oil flowed through the strait before the war started on Feb. 28.

“We feel very similar about (how) we want it to end,” the president said with Xi at this side. “We don’t want them to have a nuclear weapon.”

White House officials say Xi was also opposed to any implementation of tolls on vessels crossing the strait and expressed interest in China potentially purchasing US oil to reduce Chinese dependence on Gulf oil in the future.

Trump earlier this week had downplayed the importance of talks with Xi on the 11-week-old Iran war that has led to surging energy prices and threatens to plunge the global economy into recession if the conflict does not conclude soon.

But before Air Force One could land in Beijing, Rubio said administration officials would make the case to the Chinese officials about why they should be invested in prodding Iran to come to terms to end the war.

Indeed, the Chinese, who have been critical of the U.S. and Israeli bombardment of Iran, hold unique leverage as Iran’s biggest trading partner. The Chinese government has managed to weather the economic damage caused by the war with the help of its strategic oil reserves, but that backstop is not limitless. Economists say the Iran conflict could still have a big impact on China’s export-driven economy.

Taiwan Remains the Most Important Issue for China
Xi's sharp language on Taiwan loomed large over the visit, with Chinese government officials amplifying that differences on the self-ruled island pose the biggest risk to US-Chinese relations.

But Secretary of State Marco Rubio told NBC News that U.S. policy toward Taiwan was “unchanged” and cautioned that it would be “a terrible mistake” for China to try to take Taiwan by force. He also framed Xi's comments as standard practice.

“They always raise it on their side. We always make clear our position, and we move on to the other topics,” said Rubio, who was among the senior aides to join Trump for the talks.

China, in recent weeks, has sought to put more focus on its view that Taiwan sits at the “core” of its interests and is key to ensuring a stable relationship with the US. Trump at moments has shown ambivalence toward Taiwan, raising speculation that he could be open to loosening ties with Taipei.

Trump has demanded Taiwan increase defense spending, and in December, the White House announced an $11 billion weapons package for Taiwan, the largest ever to the island democracy.

But the US has yet to begin fulfilling the arms sales, and Trump had said he expected to discuss the matter with Xi in Beijing. He’s also groused that Taiwan “stole” America’s semiconductor business and called on Taiwan to pay the US for protection.