Kushner's involvement in the proposed back channel was first reported by The Washington Post, which said he suggested using Russian diplomatic facilities for the discussions, apparently to make them more hard to monitor.
Shortly after Trump's remarks on Twitter, Homeland Security secretary John Kelly made the rounds of Sunday television news shows to praise any so-called backchannel communications, especially with Russian Federation, as "a good thing".
Just back from his nine-day trip to the Middle East and Europe, Trump dismissed recent reports as "fake news".
And Mr Trump, who had been uncharacteristically quiet on Twitter during his nine-day trip overseas, resumed tweeting on Sunday, dismissing allegations of Russian Federation ties as "fake news" and "fabricated lies".
Even when authorized, top officials in the Trump White House frequently request anonymity to brief reporters "on background", meaning their names will not be disclosed.
The President has publicly come out in support of Mr Kushner, saying: "I have total confidence in him".
- Donald J. Trump (@realDonaldTrump) May 28, 2017 British Prime Minister May was very angry that the info the United Kingdom gave to USA about Manchester was leaked.
"It's both normal, in my opinion, and acceptable", Kelly said.
"Any channel of communication, back or otherwise, with a country like Russian Federation is a good thing", Kelly said. Michael Flynn, since fired as the president's national security advisor for his Russian associations, was also at the meeting.
Mr Trump tweeted on Tuesday: "Russian officials must be laughing at the USA & how a lame excuse for why the Dems lost the election has taken over the Fake News".
The FBI is interested in the details of Kushner's meeting with Kislyak, a meeting that the White House first disclosed in March.
The White House is bracing for the upcoming congressional testimony of former Federal Bureau of Investigation chief James Comey. "Very bad for U.S. This will change", He tweeted at about 7 a.m. ET.
Schiff said the government needed to "get to the bottom" of the matter and urged a review of Kushner's security clearance "to find out whether he was truthful".
The wider investigation into Russia's alleged election meddling is being led by Robert Mueller, a respected former FBI director who was given broad powers to pursue the case as a special counsel.
The president's son-in-law and senior adviser Jared Kushner is now a focus of the investigation into possible collusion between Trump's associates and Moscow. Some foreign affairs experts said the move, while former president Barack Obama had weeks left in his term, anxious them that it could undermine US security and some opposition Democrats have suggested that Kushner's security clearance should be revoked.