• The U.S. and China agreed to extend trade negotiations by two days, amid optimism on both sides.
  • "I think we're making a lot of progress," Trump said during an Oval Office meeting with China's vice premier, adding that there was a "very good chance a deal could be made." 
  • Trump also confirmed reports that he is planning a meeting with Chinese president Xi Jinping at his Mar-a-Lago resort in Florida next month.

Chinese President Xi Jinping delivered an optimistic message to President Donald Trump in a letter Friday, calling on the U.S. and China to redouble their efforts to meet halfway on a trade deal that has been the subject of high-level bilateral meetings this week in Washington. 

Trump was more tepid in his response to reporters, saying that the while the U.S.' relationship with China has been good, "who knows" whether a final deal will be made.

Trump's Oval Office meeting Friday afternoon with Chinese Vice Premier Liu He followed reports that the U.S. and China are considering a late-March meeting between Trump and Xi at the president's Mar-a-Lago golf resort in Florida. Trump confirmed that he will "probably" meet Xi at his resort next month. 

Treasury Secretary Steve Mnuchin also announced Friday that Chinese negotiators would extend their visit to Washington by two days in order to build on the progress that has been made so far this week. 

Mnuchin said that the March meeting, reported earlier by CNBC, may depend on the outcome of the next few days of negotiations.

China's Vice Premier Liu He turns with U.S. Trade Representative Robert Lighthizer during a meeting with U.S. President Donald Trump in the Oval Office at the White House in Washington, February 22, 2019.

"I think we're making a lot of progress," Trump said, adding that there was a "very good chance a deal could be made." 

Liu echoed Trump's outlook, saying that a trade deal was "very likely" from China's perspective.

Markets, which initially pared their gains on reports of Trump's remarks after the meeting with Liu, quickly recovered as both sides of the ongoing trade negotiations signaled that a trade deal was on the horizon.

U.S. Trade Representative Robert Lighthizer, who also attended the Oval Office meeting, said negotiations had moved forward, but noted that "a few very big hurdles" remained. 

Trump also said he would be willing to extend the March 1 deadline previously set for the trade talks to conclude, "if I see substantial progress being made." He added, "If we're doing well, I could see extending that."

Towards the end of the press event, Trump and Lighthizer publicly sparred over what to call the agreement currently being negotiated. Traditionally, bilateral trade deals between nations have been inked with memoranda of understanding, or MOUs rather than legally binding contracts, given the diversity of legal systems around the world.

"An MOU is a contract, it's the way trade agreements are generally used," Lighthizer said in response to a reporter's question about whether the MOU currently being hashed out between the U.S. and China would be short term or longer term.

"I disagree," Trump replied. "I think that a MOU is not a contract to the extent that we want...To me the final contract is really the thing, Bob. To me, MOUs don't mean anything.''

Rather than openly disagree with the president in public, Lightheizer simply agreed to call the same deal by a different name.

"From now on, we're not using the term memorandum of understanding anymore," Lighthizer said. "We're going to use the term trade agreement. We'll have the same document, but it's going to be known as a trade agreement." 

While the two sides remain far from reconciling their disputes over forced technology transfers and what the U.S. alleges is China's theft of its intellectual property, sources confirmed to CNBC on Friday that China has committed to buying $1.2 trillion in U.S. goods.