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From Trevor Hannect Me Me Cho

BEIJING, May 14 (Reuters) - Chinese President Xi Jinping told his U.S. counterpart Donald Trump on Thursday that trade talks were making progress at the start of a two-day summit, but warned that the dispute over Taiwan could push relations down a dangerous path and even into conflict.

The Chinese Foreign Ministry said Xi's remarks about Taiwan, a democratically governed island that China claims as part of its territory, came during a closed-door meeting that lasted more than two hours between the leaders of the world's two largest economies.

These remarks represented a strongly worded, if not unprecedented, warning during an official event that appeared friendly and relaxed, but Taiwan was not mentioned in the US statement about the talks.

The statement, on the other hand, focused on the two leaders’ shared desire to reopen the Strait of Hormuz, and on Xi’s clear interest in buying American oil to reduce China’s dependence on Middle Eastern supplies.

With Trump's popularity waning due to the ongoing war with Iran, the first visit by a US president to China in nearly a decade has taken on added significance as he seeks to achieve economic gains.

After a ceremony that included a review of the honor guard and crowds of children waving flowers and flags in the Great Hall of the People, Trump said, "Some people are saying this could be the biggest summit ever."

The Chinese Foreign Ministry said in a statement that Xi told Trump that preliminary talks, held by South Korea's economic and trade teams on Wednesday, had reached a "generally positive and balanced outcome".

Officials said the aim of the latest round of negotiations was to maintain the trade truce agreed upon last October and to put in place mechanisms to support trade and investment in the future.

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Trump expressed his expectation this week that Xi would raise the issue of US arms sales to Taiwan. With the fate of a $14 billion deal awaiting Trump's approval still uncertain, China reiterated its strong opposition to the sales on Wednesday.

The United States is legally obligated to provide Taiwan with the means to defend itself, despite the absence of formal diplomatic relations between them.

The Chinese statement on the talks said that Xi told Trump that Taiwan was the most important issue facing them, and that mishandling it could push the entire US-China relationship into a very dangerous situation, leading to a clash or even a conflict between the two countries.

Joe Mazur, a geopolitical analyst at Trivium China, a consulting firm, described Xi's remarks as noteworthy, even though Beijing has previously issued strongly worded warnings about Taiwan.

Mazur added, "He (Xi) is warning the American side very clearly against tampering."

Trump, posing for photos with Xi afterward at the Temple of Heaven, did not respond to a reporter's question about whether they had discussed Taiwan. The temple is a UNESCO World Heritage Site. Xi and Trump are scheduled to attend a state banquet on Thursday before having tea and lunch together on Friday.

The Chinese statement said that Trump and Xi agreed to expand cooperation in trade and agriculture, and exchanged views on the situations in the Middle East, Ukraine and the Korean Peninsula.

The White House said the two leaders discussed expanding access for American companies to the Chinese market and increasing Chinese investment in American sectors.

Trump is accompanied on this trip by a group of CEOs seeking to resolve issues with China, including Elon Musk and Nvidia CEO Jensen Huang, who joined the trip at the last minute. China views Musk as a visionary, and at times as malevolent.

Reuters reported exclusively that the United States has allowed about 10 Chinese companies to purchase Nvidia's powerful H200 artificial intelligence chips, but they have not yet received any shipments.

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Ali Wein, senior adviser on US-China relations at the International Crisis Group, said that the power dynamics have changed since Trump’s recent visit to Beijing, when China went to great lengths to woo Trump and buy billions of dollars’ worth of American goods.

Wayne added, "At that time, China was trying to convince the United States of its growing status... This time, it is the United States that is recognizing this status of its own volition."

They noted that Trump revived the term “G2,” or the Group of Two, referring to the two superpowers, when he last met Xi on the sidelines of the Asia-Pacific Economic Cooperation (APEC) forum meeting in South Korea in October.

Trump enters the negotiations from a position of weakness. US courts have limited his ability to impose tariffs at will on exports from China and other countries. Furthermore, the trade war with Iran has fueled inflation domestically and increased the likelihood that Trump's Republican Party will lose control of one or both houses of Congress in the November midterm elections.

Despite the Chinese economy's struggles, Xi does not face similar economic or political pressures.

However, both sides are keen to maintain the trade truce, under which Trump suspended hefty tariffs on Chinese goods, and Xi backed down from choking off global supplies of rare earth minerals, which are vital to the manufacture of products ranging from electric cars to weapons.

Officials said Washington is looking to sell Boeing aircraft, agricultural goods and energy products to China to reduce the trade deficit that bothers Trump, while Beijing wants the United States to ease restrictions on exports of advanced chip-making equipment and semiconductors.

Aside from trade issues, Trump is expected to urge China to persuade Iran to reach an agreement with Washington to end the conflict. However, analysts doubt Xi is willing to pressure Tehran or end support for its military, given Iran's importance to Beijing as a strategic counterweight to the United States.

U.S. Secretary of State Marco Rubio told Fox News aboard Air Force One that it was in China's interest to help resolve the crisis, as many of its ships were stuck in the Gulf, and a slowdown in the global economy would hurt Chinese exporters.

Trump invited his Chinese counterpart to visit the White House on September 24, during a state banquet hosted by Xi in honor of Trump in Beijing.