Xi greeted Trump with pageantry at the imposing Great Hall of the People, next to Tiananmen Square, on the second day of his visit to China -- the critical stop in a five-nation tour of Asia.
The two leaders have stepped up the flattery but the US president was expected to prod Xi to make more efforts to slash China's massive trade surplus with the United States and curb its economic ties with North Korea.
"Our meeting this morning... was excellent in discussing North Korea and I do believe there's a solution to that, as you do," Trump said as he sat across from Xi.
He did not elaborate on what the solution might be but his administration believes that China's economic leverage over North Korea is the key to strongarming Pyongyang into halting its nuclear weapons and missile programmes.
Xi, who has repeatedly urged the United States and North Korea to hold negotiations to resolve the crisis peacefully, told Trump that their nations should "strengthen communication and coordination in major international and regional issues including the Korean Peninsula and Afghanistan".
The trip comes as Trump faces the lowest approval ratings for a US president in seven decades, and with the one-year anniversary of his election Wednesday spoiled by big Democrat wins in state and mayoral votes.
Meanwhile, Xi cemented his status as the most powerful Chinese leader in a generation at a Communist Party congress last month, when his name was inscribed into the constitution.
On Trump's first state visit to China, a military band played the US and Chinese anthems, ceremonial cannon fire erupted, and the two leaders reviewed a military honour guard just across from Tiananmen Square -- the site of the army's deadly crackdown on pro-democracy protesters in 1989.
Children waved US and Chinese flags at the two leaders, a day after Xi treated Trump to a tour of the Forbidden City, capped by an opera performance and a private dinner.
"Emphasising pomp over substance is the Chinese way. With President Trump, they think that the state-visit plus treatment will impress him and buy China some goodwill," Bonnie Glaser, China expert at the Center for Strategic and International Studies in Washington, told AFP.
- 'Beautiful welcome' -
Evidently pleased with the first day of his visit, Trump circumvented China's internet censorship system to post a message to Xi on Twitter, which is banned in the country.
"THANK YOU for the beautiful welcome China! @FLOTUS Melania and I will never forget it!" wrote Trump, who also posted an AFP photo of his visit.
Both leaders say they have struck up a friendship since Trump hosted Xi for a plush visit at the billionaire's Mar-a-Lago resort in Florida for their first meeting in April.
"My feeling toward you is an incredibly warm one. As we said there's great chemistry and I think we're going to do tremendous things for both China and the United States," Trump told Xi on Thursday.
Despite the public bonhomie, the two leaders are expected to have tough discussions behind closed doors.
"The flattery will not have significant substantive effect," said Sam Crane, a Chinese history expert at Williams College.
But the pageantry is helpful to Xi's consolidation of power at home, Crane said.
"Symbolically all of this is being framed in China as Trump coming to pay homage to the 'core' leader," he said.
- 'Cannot support' Pyongyang -
Xi and Trump will oversee a signing ceremony for massive deals between US and Chinese companies, but the yawning trade imbalance is likely to remain a concern.
Trump said previous US administrations had let the trade imbalance get "out of kilter".
"We will make it fair and it will be tremendous for both of us," he said.
Trump will also seek greater efforts from Xi to go beyond UN sanctions on North Korea.
Before arriving in Beijing, Trump used a speech at the South Korean parliament to urge China and Russia to fully implement UN sanctions, downgrade diplomatic relations, and sever all trade and technology ties with the North.
He later tweeted a warning to North Korea to avoid "a fatal miscalculation. Do not underestimate us. AND DO NOT TRY US."
Though China has backed the UN sanctions, US officials want Chinese authorities to clamp down on unauthorised trade along the North Korean border.
"Without them really participating lock, stock and barrel in this it's not going to work," a senior US official said.
But experts doubt China will take the kind of steps that Trump wants, such as halting crude oil exports to the North. Beijing fears that squeezing Pyongyang too hard could cause the regime to collapse.
"Xi might 'do more' on North Korea but he will never do as much as the US wants, because (China) has a strong interest in maintaining regime stability in North Korea," Crane said.
"I suspect Xi will continue to press Trump to open up negotiations with Kim as a price for China to 'do more' on North Korea."