Mr Tillerson met the Chinese leader in Beijing's Great Hall of the People, as his East Asian tour comes to an end.
Mr Xi said he was glad to see good progress from Mr Tillerson's meetings.
"You said that China-US relations can only be friendly. I express my appreciation for this," he said.
Mr Xi added that he had spoken to the US president several times.
"We are both expecting a new era for constructive development," he said.
Mr Tillerson said Mr Trump places a "very high value on the communications that have already occurred".
There was no mention of contentious issues like North Korea's missile and nuclear programmes, or the status of Taiwan, which China claims as its own.
The meeting came as North Korea's military tested a new high-thrust engine, according to reports from Pyongyang's state news agency.
Washington wants China, the North's main trading partner, to use its influence to curb the weapons programmes.President Trump tweeted his frustrations on Friday, writing: "North Korea is behaving very badly. They have been "playing" the United States for years. China has done little to help!"
Negotiations are under way for a potential first summit meeting between Mr Xi and Mr Trump next month in the US.
Mr Trump has been a vocal critic of China in many areas - including its exchange rate policy and its operations in the South China Sea.
However, he soothed ruffled feathers to some degree in February by agreeing to honour the so-called "One China" policy, which states that there is only one Chinese government.
The leaders' US encounter could now hold the key to future power-plays between the world's two largest economies.