Some Democrats have called on Kushner to be stripped of his security clearance and have asked the Federal Bureau of Investigation to review whether Kushner complied with the law.
Economic adviser Gary Cohn said: "We're not going to comment on Jared".
"If not, then there's no way he can maintain that kind of a clearance", Schiff said.
The White House declined to comment Saturday on a news report that top President Trump adviser Jared Kushner had at least three undisclosed conversations previous year with Russian ambassador Sergei Kislyak.
The New York Times reported that Russian officials discussed finding backdoor ways to influence Trump without his knowledge through retired Lieutenant Gen. Michael Flynn and former Trump campaign manager Paul Manafort.
The person wasn't authorized to publicly discuss private policy deliberations and spoke on condition of anonymity.
Russia, a pivotal player in Syria, has backed Syrian President Bashar Assad, often at the expense of civilians and at odds with USA policy during Syria's long civil war.
And while this is yet more bad news for the Trump White House, a report from Politico today says that within those walls, "there is a feeling of resentment among people about Kushner's special status as a family member, and a feeling that it's about time for him to have a turn under the gun".
Officials in the White House have also believed to have held discussions about setting up a "War Room" to shield the day-to-day running of the presidency from the various investigations underway. "What's worrying me are the patterns we're seeing. And the other pattern we have is just a continuous drumbeat of inappropriate contacts with the Russians".
Those feelings were present even before he came under fire for his proposal to establish a back-channel connecting Trump's campaign and Russian Federation in December, which came to light this week. If true, the Times' report appears to be inconsistent with the narrative that Trump was engaged in a quid-pro-quo with Russia, as alleged by the infamous Trump dossier that some liberals have used to accuse Trump of colluding with the Russians.More news: Lindsey Graham skeptical of report on Kushner, Russians
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Following Comey's firing, the White House was besieged by a slew of negative news stories that raised further questions about the president's and his associates' ties to Russian Federation. Flynn apparently would have been the USA point person, the source said. He added: "It allows you to communicate in a discreet manner".
Lt. Gen. H.R. McMaster, the National Security Adviser, on Saturday declined to say whether he would be concerned if a private citizen attempted to set up backchannel communications with a foreign government to influence USA foreign policy and said he would not be concerned if a White House official attempted to do so, reports CNN. "Any way that you can communicate with people, particularly organizations that are maybe not particularly friendly to us is a good thing".
According to reports, Ivanka is not sold on life in Washington, DC.
The newspaper cited anonymous United States officials who were briefed on intelligence reports on intercepted Russian communications.
The Post said Kislyak reportedly was taken aback by the idea of having an American use Russian communications equipment at one of its facilities because it could have involved security risks for both Americans and Russians.
No such network was necessary, the administration decided, after Rex Tillerson was confirmed as secretary of state - moving toward more official communications channels with Moscow.
The news agency anonymously cited current and former USA officials. Sally Yates, the former acting attorney general, told Congress this month that that deception left Flynn vulnerable to being blackmailed by the Russians. He was interviewed by the Federal Bureau of Investigation in January about his contacts with Kislyak. Kislyak also attended a Trump campaign speech in Washington in April 2016 that Kushner attended. The White House did not respond to a request for comment.
The US intelligence community concluded in January that Russian Federation tried to influence the presidential election in favor of Trump, including through an aggressive hacking campaign against senior Democrats.
"Trump has no choice but to immediately fire Kushner, whose failure to report this episode on his security clearance is reason enough for a criminal investigation", the Deputy National Committee deputy communications director Adrienne Watson demanded in a statement.