Trump also offered to host a "Western-style" dinner for Xi on December 1, after the G20 leaders' meeting, an invitation that Beijing had tentatively accepted, people familiar with the matter told the South China Morning Post.
"Those discussions are moving along nicely", Trump wrote on Twitter Thursday.
The push for a possible deal with China was prompted by the president's telephone call with Xi on Thursday, sources in Washington said.
But Mr Kudlow cautioned that Mr Trump would "aggressively" pursue his agenda against China, if no deals were reached on intellectual property theft, cyber security and tariffs on commodities, among other issues.
Xi on Thursday said he looks forward to meeting with Trump in Argentina and hopes the two sides build stable relations, according to China's state media.
Neither leader specified any details of possible progress in their first known direct discussion in several months.
The Trump administration this year has already imposed tariffs on $250 billion in trade with China and is threatening to impose tariffs on all remaining imports from China, which last year were worth $505 billion.
The United States has already imposed tariffs on $250 billion worth of Chinese goods, and China has responded with retaliatory duties on $110 billion worth of US goods.
"Both leaders attach great importance to China-US ties and economic ties", Lu said.
"He wants to do it", Trump said of Xi.
"What negotiations have lacked to date has been that (presidential) level of engagement".
"The Trump administration should not miscalculate China's tolerance for what they perceive as bullying tactics", he said. It also fuelled speculation that Chinese Vice-Premier Liu He's trip to the USA, which had originally been scheduled for September but was cancelled due to the escalation of the trade dispute, might be back in the cards.
Trump said that in early October China wanted to come in and make a deal, but he told them they weren't ready.
"The best situation (from a Trump-Xi meeting) would be no further actions, temporarily". "President Xi Jinping also stressed that China-U.S. trade has always been serving as ballast and a stabilizer for China-US relations".
Fujian Jinhua Integrated Circuit Co and Taiwan's United Microelectronics Corp were indicted along with three individuals, the Justice Department said.
This week, prosecutors announced an indictment against 10 defendants, including two Chinese intelligence officers and other computer hackers and co-conspirators, who are all accused of breaking into American company computers to steal data on a turbo fan engine used in commercial jetliners.
'We talked about many subjects, with a heavy emphasis on Trade. He said further meetings with Xi are being scheduled for the G-20 summit of the world's biggest economies, set for November 30 in Buenos Aires, the first ever such summit in South America.
Bloomberg reported on Friday that Trump wants to reach a trade agreement with China at the G20 meeting.