That Trump is privately questioning Pence's loyalty seems a further indication of the president's growing isolation in recent weeks.
"We had a good laugh and the president said to me "there are no anonymous sources that would say what that article said". "It's fake news, and that's what breaks up a country".
Trump was asked about a report which appeared in Friday editions of the Times.
"As a husband and father, I was offended by the words and actions described by Donald Trump in the 11-year-old video released yesterday", Pence said in a statement at the time. A typical New York Times phony story.
Vice President Mike Pence warned Saturday that USA sanctions and pressure on China would remain in place until Beijing reforms its trade practices.
Trump, who is known to hold personal loyalty as a deciding factor in many of his friendships and hiring decisions, referred to the vice-president as "a trooper" and "a terrific person" who has "already been tested, in many ways".
"The New York Times did a phony story, as usual, about my relationship with [Pence]", Trump tweeted Saturday morning.
After his meeting with United States Vice President Mike Pence, Taiwan envoy Morris Chang (張忠謀) also met several other leaders at the Asia Pacific Economic Cooperation (APEC) summit in Papua New Guinea Saturday.
A reporter appeared to surprise the president last week, at a post-midterms press conference, when he asked if Trump was planning on having Pence be his running mate again in 2020.
Xi called on the U.S. to try to resolve issues through consultation based on the principle of "equality", warning the USA against escalating tensions and potential damage to global trade.
The president added: "You know what the quote would be?"
"The South China Sea doesn't belong to any one nation, and you can be sure: The United States will continue to sail and fly wherever global law allows and our national interests demand", Pence said.
"We believe that progress could be made between our two nations, even as the United States remains in a strong position", Pence said.