Russian President Vladimir Putin at a meeting on 16 July in Helsinki gave the American leader is Donald Trump papers with a proposal to extend for five years the Treaty on the limitation of nuclear arsenals.
The White House said Trump had provided Paul with a "letter of introduction" for his trip at the senator's request. The White House plans to impose sanctions over foreign interference in U.S. elections, The Washington Post said.
Both Trump and Putin have invited each other to their respective capital cities in the aftermath of last month's Helsinki summit between the two leaders.
Trump has pushed for easing tensions between the former Cold War foes, exacerbated by US intelligence findings that Russian Federation meddled in the 2016 presidential election, trying to tilt the outcome to Trump.More news: Critics of nation-state law 'mistaken and misinformed,' Netanyahu advisor says
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CNN aired round two of its panel of Trump voters - split down the middle with three who still support the president and three who regret their 2016 vote - and this time, the topic was a hot one: Russian Federation.
The White House again refused to answer questions about what was taken about during the summit but would neither confirm or deny the validity of the document.
But Peskov said the Kremlin had not familiarized itself with the contents. However, he undermined those remarks when he quickly returned to calling the special counsel's investigation a "witch hunt", and referred to Russian interference as a "hoax".
A United States official provided to CNN the text of the letter, which read: "I would like to introduce Senator Rand Paul of Kentucky, a member of the Senate Foreign Relations Committee, and a voice for expanding dialogue with the Russian Federation". Trump's top intelligence official, Dan Coates, has said that he is in the dark about what Trump discussed with Putin in their one-on-one meeting in Helsinki. "He is interested in legislative exchanges, parliamentary dialogue and cultural and educational exchange programs, increased counter-terrorism cooperation, building on recent successes like the disruption of the St. Petersburg plot and resolution of the military conflicts in Syria and Ukraine".