Trump, who remained at his Mar-a-Lago resort for the weekend after Xi's departure, was visiting his nearby Trump International Golf Club in West Palm Beach, Fla.at the time of the tweets.
Trump's aides insisted he had made good on his pledge to raise concerns about China's trade practices and said there was some headway, with Xi agreeing to a 100-day plan for trade talks aimed at boosting U.S. exports and reducing China's trade surplus with the United States.
USA president Donald Trump has said his meetings with China's president Xi Jinping went well but regarding progress on trade "only time will tell".
Mr Trump has repeatedly criticised China for exporting more to the U.S. than it buys.
United States industry had hoped Trump would deliver a strong message to Xi behind closed doors to end what they see as discriminatory trade policies, but not do anything rash to spark a trade war.
The friendly tone was a far cry from Trump's acerbic campaign denouncements about China's "rape" of the United States economy and his vow to punish Beijing with punitive tariffs.
Xi landed in Alaska for a refueling stop following his meeting with President Donald Trump earlier Friday in Florida.
"We have engaged in deeper understanding, and have built a trust - a preliminary working relationship and friendship", he said. Trump accepted, with a date yet to be determined.
"Both the atmosphere, the chemistry between the two leaders was positive", said U.S. Secretary of State Rex Tillerson at a press briefing.
"All of us are feeling very good about the results of this summit".
The meeting of the leaders of the world's two largest economies was largely overshadowed by the US missile strikes on Syria.
Six people arrested after deadly St. Petersburg subway bombing
Investigators are apparently examining links between the arrested men and Monday's alleged bomber, 22-year-old Akbarzhon Jalilov. In the past two decades, Russian trains and planes have been frequent targets of attack, usually blamed on Islamic militants.
The US began the deployment of the sophisticated missile defence system in South Korea last month to counter North Korea's increasing aggression in the region. "We would be happy to work with them", he said.
Asked to elaborate, he said simply: "I would just say we view sanctions as being a very important tool, whether it's North Korea or whether it's Syria". In an editorial, the paper said Trump launched the strike "to establish his authority as the US president". Its U.N. ambassador, Liu Jieyi, never mentioned the suspected chemical weapons attack in Syria, or the USA airstrikes, at an emergency meeting of the U.N. Security Council on Friday.
In a statement late on Saturday, the US Navy's Third Fleet said the strike group had been directed to sail north, but it did not specify the destination.
"Why have you attacked the Syrian army which is at war with terrorists?" It was the first direct United States assault on the Russian-backed government of Syrian President Bashar al-Assad in six years of civil war.
There appeared to be little in the way of concrete achievements during 24 hours in the sun, but officials said that a rapport had been built that will carry on the next four years.
On Thursday night, conservative US news media painted the Syria hit as a bold but calculated warning to China.
"We had a long discussion already. Absolutely nothing", he said to laughs from the delegation. The relationship developed by President Xi and myself I think is outstanding.
First lady Melania Trump and Peng Liyuan (puhng LEE'-yoo-en), the wife of Chinese President Xi Jinping (shee jihn-peeng), visited a seventh-grade civics class at a Florida middle school. But they offered no details about how they planned to achieve that.
The only other foreign leader to be hosted at Mar-a-Lago during Trump's presidency so far is Japanese Prime Minister Shinzo Abe, a close US ally.
In return, Xi hoped to obtain assurances from Trump on punitive tariffs and the delay of an American arms sale to Taiwan, at least until after a major Communist Party meeting later this year.