By Trevor Hannicht and Liz Lee

BEIJING, May 15 (Reuters) - U.S. President Donald Trump began final talks with Chinese President Xi Jinping on Friday, touting economic achievements that generated little excitement in the markets, while Beijing warned Washington against mishandling the Taiwan issue and said that a war with Iran should never have happened.

Trump is making the first visit by a sitting US president to China, the United States' main strategic and economic rival, since his previous visit in 2017. He is seeking tangible results to boost his approval ratings ahead of the midterm congressional elections.

Trump said, "We've made some great trade deals, and they're great for both countries."

During a meeting between the two leaders for tea and lunch, the Chinese Foreign Ministry issued a frank statement expressing its disappointment over the Iran war.

The ministry said, "This conflict, which should never have happened, has no reason to continue," adding that China supports efforts to reach an agreement to end a war that has severely affected energy supplies and the global economy.

Trump stated that he discussed Iran with Xi and that they found their views to be "very similar." Xi did not comment on this.

Trump was expected to urge China to persuade Iran to reach an agreement with Washington to end a war that has driven up prices and left him in a weak political position at home.

But analysts doubt that Xi is prepared to put significant pressure on Tehran or end support for its military, given Iran's importance to Beijing as a strategic counterweight to the United States.

A U.S. summary of the talks held on Thursday highlighted what the White House described as the two leaders' shared desire to reopen the Strait of Hormuz, as well as Xi's apparent interest in buying U.S. oil to reduce China's dependence on Middle Eastern supplies.

Typically, one-fifth of the world's oil and liquefied natural gas supplies passed through the strait.

Boeing shares fall due to disappointing deal

US officials said the two sides also agreed on deals to sell agricultural products, beef, and energy to China, and made progress in establishing mechanisms to manage trade in the future. The two sides are expected to identify $30 billion worth of goods that will not be subject to restrictions.

However, few details were available about the deals, and there were no signs of progress on the sale of Nvidia's advanced H200 AI chips to China, despite CEO Jensen Huang joining the visit at the last minute.

Trump told Fox News that China had agreed to order 200 Boeing aircraft, its first purchase of American-made commercial planes in nearly 10 years, but that number was far less than the 500 planes the market had anticipated. Boeing shares fell by more than four percent.

Perhaps the summit's main achievement will be preserving the fragile trade truce reached when the two leaders last met in October, with Trump suspending tariffs of more than 100 percent on Chinese goods, while Xi backed down from cutting off supplies of critically important rare earth elements.

U.S. Trade Representative Jamieson Greer, who accompanied Trump, told Bloomberg Television on Friday that it had not yet been decided whether the truce would be extended beyond its expiration later this year.

* Stern warning regarding Taiwan

Xi’s remarks to Trump that mishandling the Taiwan issue could lead to conflict represent a sharp and perhaps unprecedented warning during an otherwise cordial and relaxed summit.

The issue of Taiwan, the democratically governed island that Beijing considers its own and which lies only 80 kilometers from the Chinese coast, has long strained relations between the United States and China, as Beijing refuses to rule out the use of force to control the island, while Washington is legally obligated to provide Taipei with the means necessary to defend itself.

"U.S. policy on the Taiwan issue has not changed to this day," U.S. Secretary of State Marco Rubio, who is accompanying Trump, told NBC News, adding that the Chinese "are always raising this issue... and we are always making our position clear and moving forward."

Taiwan's Foreign Minister Lin Chia-long thanked the United States on Friday for its repeated expressions of support.

Xi said at a lavish state dinner on Thursday that the relationship between China and the United States is the most important in the world, adding, "We must make it work and never spoil it."

* Imprisoned Chinese dissident Jimmy Lai

Rubio said Trump raised with Xi the case of Hong Kong's most prominent critic, media mogul Jimmy Lai, who was sentenced in February to 20 years in prison in the biggest national security case in the Asian financial hub.

"The president always brings up this issue and some other issues, and obviously we'll be hoping for a positive response," Rubio told NBC News.

He added, "We are open to any arrangement that suits them, as long as he gets his freedom."

The Chinese Foreign Ministry had previously responded when asked about Lai by saying that Hong Kong affairs were an internal matter for Beijing.