America Media (which owns National Enquirer) COO Dylan Howard responded in a statement: "At the beginning of June, we accurately reported a story that recounted the relationship between Joe Scarborough and Mika Brzezinski, the truth of which is not in dispute".
They also claimed that the White House had tried unsuccessfully to get them to apologise to the president for unfavourable coverage in exchange for him getting a negative tabloid story about them killed.
Trump's use of social media - specially Twitter - was found problematic by his aides during his presidential campaign, which he had tended to send off incendiary posts and off-the-script remarks at election rallies. The source said Kushner answered: "Well, then maybe you should apologize".
The president appears to have woken up angry at the media Saturday as he sent out three tweets in quick succession about cable news channels.
He referred to her co-host Joe Scarborough, a former Republican U.S. congressman, as "Psycho Joe".
Trump responded Friday, calling the show "FAKE NEWS".
Brzezinski and Scarborough dismissed as lies Trump's claims, made in the Thursday Twitter messages, that he refused to have dinner with them or that Brzezinski had had a face lift.
International Yoga Day celebrated in Pakistan too
Bollywood actor Jackie Shroff and social activist Shantilal Mutha also attended the hour-long yoga session organised in Worli. He said Yoga's popularity is high even outside India; and Yoga has connected the world with India.
When asked about the tweet, House Speaker Paul Ryan said, "Obviously, I don't see that as an appropriate comment".
Crazy Joe Scarborough and dumb as a rock Mika are not bad people, but their low rated show is dominated by their NBC bosses.
"I know Melania. I haven't talked to her in months, but if my gut is right, I don't think she's going to put up with it much longer", Ms Brzezinski said. "I said no!" Trump wrote in a series of tweets.
Scarborough replied, saying he has texts and phone records to prove his account of the story. He added: "Why do you keep lying about things that are so easily disproven?"
This comes after outrage earlier this week when he directed blatantly sexist attacks against Brzezinski, insulting her appearance and intelligence.
"I am very concerned as to what this once again reveals about the president of the United States", said Brzezinski, who is engaged to be married to Scarborough. Scarborough tweeted. "What is wrong with you?"