The probe into Russia's role in the USA election pierced the innermost circle of the White House on May 27, with reports that Donald Trump's son-in-law sought a secret communications line with Moscow - the most damning allegation yet from the scandal.
Meanwhile, Trump, returning from a nine-day diplomatic tour in the Middle East and Europe, resumed a Twitter tirade about domestic issues on Sunday, calling alleged leaks from the White House lies created by the "fake news media" as sources have remained unnamed.
The newspaper cited anonymous U.S. officials who were briefed on intelligence reports on intercepted Russian communications.
"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.
Under the planned shakeup, White House Press secretary Sean Spicer would take a diminished public role, while Mr. Trump would take more opportunities to engage directly with his supporters via campaign rallies, social media appearances such as Facebook Live videos, and interviews with friendly news organisations, the NYT reported.More news: Vettel wins in Monaco to extend his F1 lead
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Some Democrats said Kushner's national security clearance might have to be revoked.
CNN reported on Thursday that the Federal Bureau of Investigation was looking into Kushner's many roles on both Trump's transition team and in the White House. "What that allows you to do is communicate in a discrete manner". Both outlets have reported that Trump and his advisers are considering a shake-up of his senior staff in an attempt to contain the escalating problems caused by the various investigations into Russian meddling during the 2016 campaign. Trump worked the phones with various lawyers and advisers on Sunday, one of the White House officials said.
He has told friends that he and his wife, Ivanka, have made no long-term commitment to remain by Trump's side, saying they would review every six months whether to return to private life in NY.
Schiff also said that even if the topic of Kushner's secret communication was about how best to resolve the years-long conflict in Syria, that doesn't mitigate the situation because Russia's objectives are different from those of the USA - especially given the intelligence on Russia's interference in the election.
The Senate Intelligence Committee, which is investigating Russia's meddling in the 2016 United States presidential election, has requested information and documents from Mr Trump's campaign.
Kushner's involvement in the proposed back channel was first reported by The Washington Post, which said he proposed using Russian diplomatic facilities for the discussions, apparently to make them more hard to monitor.
"They reached out to us yesterday to make sure that we knew that was the case and I'm sure he's willing to do so, Mr Corker said on NBC's Meet the Press". Media reports revealed the meeting, along with another private session Kushner had with a representative of a Russian bank.