Trump's longtime lawyer, Marc Kasowitz, has joined a still-forming legal team to help the president shoulder the intensifying Russian Federation investigations.
Some critics have called for Kushner's security clearance to be revoked, others say he should temporarily step aside while his ties to Moscow are being reviewed.
The Republican health care bill that narrowly passed the House faces an uncertain future in the Senate after a Congressional Budget Office analysis said it would leave 23 million more Americans uninsured by 2026. He says it's "obviously very concerning" if a key Trump campaign figure was possibly seeking secret communications with Russian Federation.
In an apparent dig at the USA intelligence community, Trump also tweeted yesterday that British Prime Minister Theresa May was "very angry" about the leaking of information the United Kingdom gave to the US about last Monday's terrorist bombing outside an Ariana Grande concert in Manchester.
"But for people associated with the campaign after that campaign has ended and where the Russians during that campaign were helping you, to try to establish a back channel and hide it from your own government, that's a serious allegation", he said.
Mr Kushner initially had come to the attention of FBI investigators past year as they began scrutinising former national security adviser Michael Flynn's connections with Russian officials, two sources told Reuters.
"They need to quarantine this stuff and put the investigations in a separate communications operation", said Jack Quinn, who served as White House counsel for President Bill Clinton. The person, like others, spoke on condition of anonymity in order to discuss private conversations.
Trump has frequently dismissed his campaign's connection with Moscow as an excuse made up by Democrats to explain his stunning upset win for the White House over Democrat Hillary Clinton, a former USA secretary of state.More news: Macron finally speaks out about the Trump handshake: "it wasn't innocent"
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Kushner would speak for himself, Corker said he'd been reassured, "when the time is right".
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. "What's worrying me are the patterns we're seeing".
Taking his outrage to Twitter, Mr Trump said it was his opinion numerous White House leaks were "fabricated lies made up by the #FakeNews media".
"Whenever you see the words "sources say" in the fake news media, and they don't mention names it is very possible that those sources don't exist but are made up by fake news writers". He remains an influential confidant within the White House, as does his wife, Ivanka Trump. Flynn was sacked in February, officials saying he misled Vice President Mike Pence about whether he and the ambassador had discussed USA sanctions against Russian Federation in a phone call.
Former director of national intelligence James Clapper took a darker view of contacts with representatives of Russian President Vladimir Putin.
Kushner, is one of Trump's closest advisers.
They include reports that Mr Jared Kushner sought a secret communications line with Moscow.
Kelly appeared on "Fox News Sunday", NBC's "Meet the Press" and ABC's "This Week," Schiff also spoke on ABC, and Booker was on CNN's "State of the Union".