In their talks on Thursday night, Xi told Trump that the two sides had to come up with a proposal to settle the trade war, while Trump said the two men had a "long and very good conversation" on several issues, including trade and North Korea.
The two countries have been locked in an escalating trade battle, with each side imposing tariffs on billions of dollars worth of imports from each side.
Markets moved higher after Bloomberg reported US President Donald Trump wants to reach an agreement with Chinese President Xi Jinping at the Group of 20 nations summit in Argentina later this month.
Asian stocks rose sharply on Friday on hopes of a trade deal between the United States and China. "We have a new deal", he said adding that the U.S. is now negotiating with the European Union, which "has absolutely hurt" the United States. "We talked about many subjects, with a heavy emphasis on Trade", Mr Trump tweeted.
"The issues driving the China-US trade tensions are complicated and contentious, which makes it incredibly hard to believe that substantive progress was made during this phone call", Boltansky said.
"The economic teams of the two countries should strengthen contact, conduct consultations on issues of mutual concern, and push for a mutually acceptable solution to China-US economic and trade issues", Xi said.
In May, after his last phone call with Xi, Trump agreed to ease up on sanctions imposed on Chinese telecom equipment maker ZTE Corp., saying they would cost too many Chinese jobs.
In recent months China has repeatedly questioned the U.S.'s sincerity in trade talks, wary of agreeing to something only to have Trump change his mind. He backed out on a deal congressional Democrats said they struck with Trump to provide legal status to young undocumented immigrants.
"We are not on the cusp of a deal", Kudlow said.
The deficit in goods and services trade with China increased to $40.2 billion for the month, the highest ever.
"There's no massive movement to deal with China", Kudlow, the director of the National Economic Council, told CNBC.
Trump's posture toward China has been closely watched by investors, who are looking for the possibility of tensions cooling.
In comments in state media, Xi said he hoped China and the United States would be able to promote a steady and healthy relationship, and that he was willing to meet Trump in Argentina.