Tillerson told top Chinese foreign policy adviser Yang Jiechi that Trump and Xi had developed a "very regular and close working relationship".
His visit, Tillerson said, also provided an opportunity to assess progress made between the sides since Xi and Trump met in April at the US president's estate in Florida.
Tillerson is making his second visit as secretary of state to the world's No 2 economy and chief American rival for influence in Asia, and increasingly, the world.
Neither Tillerson nor the Chinese officials mentioned North Korea in opening remarks made in the presence of journalists.
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Ties between Beijing and Washington are considered more crucial than ever with the standoff over Pyongyang's nuclear weapons and ballistic missiles entering a new, more dangerous phase as its leader, Kim Jong Un, and Trump exchange personal insults and threats of war with no sign of a diplomatic solution.
Although adamantly opposed to steps that could bring down Kim's regime, Beijing appears increasingly willing to tighten the screws on Pyongyang, and agreed to tough new United Nations sanctions that would substantially cut foreign revenue for the isolated North.
On Thursday, Beijing ordered North Korean-owned businesses and ventures with Chinese partners to close by early January, days after it said it would cut off gas and limit shipments of refined petroleum products, effective January 1.
It made no mention of crude oil, which makes up the bulk of Chinese energy supplies to North Korea and is not covered by the UN sanctions. China has also banned imports of North Korean coal, iron and lead ore, and seafood since early September.
Other than North Korea, the US and China have other security concerns to address. They remain at odds over Beijing's military buildup and assertive claims to disputed islands in the South China Sea.
Tillerson is also expected to restate concerns about China's massive trade surplus with the USD 347 billion last year and what American companies say are unfair barriers to investment, including pressure to hand over their technology. Washington wants Beijing to make good on its promise to let market forces have a bigger role in its economy, give equal treatment to foreign and Chinese companies and roll back state industry's dominance.
Despite his tough criticism of China's trade practices, Trump has forged a personal connection with Xi over phone calls and while hosting him in Florida, during which they agreed on four high-level dialogues to cover various aspects of relations.
The November meeting of the two leaders will be grander and more choreographed than the informal talks in Florida that were most memorable for Trump's ordering a missile strike on Syria and then informing Xi about it afterward as they ate chocolate cake.