The White House told Fox News that Paul asked Trump to write a letter of introduction to the Russian leader.
However, deputy White House spokesman Hogan Gidley said the missive was a "letter of introduction" that Trump had written at Paul's request and "mentioned topics of interest that Senator Paul wanted to discuss with President Putin".
Sen. Rand Paul announced on Wednesday that he "was honored to deliver a letter from President Trump to Vladimir Putin's administration" that he said addressed topics ranging from counterterrorism to "resuming cultural exchanges".
According to the White House, the letter 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".
Japan marks 73rd anniversary of atomic bombing of Hiroshima
A survey conducted by the Kyodo News agency showed 81 percent of the survivors want Japan to sign the Treaty on the Prohibition of Nuclear Weapons .
At the time, uncertainty about what Mr Trump and Mr Putin discussed during the private meeting in which members of the press were also banished from caused a stir.
Putin's spokesman, Dmitry Peskov, said the Kremlin has not yet examined the letter Paul presented.
Paul said Trump was right to talk to USA adversaries and called the criticism directed at Trump a reflection of "how unhinged people are in their hatred for the president".
Russian President Vladimir Putin said on July 27 that he was ready to meet US leader Donald Trump both in Washington and in Moscow. But Peskov said the Kremlin had not familiarized itself with the contents. Trump sparked outrage by accepting Putin's word over that of his intelligence agencies at a Helsinki news conference.
Chinese exports accelerate as USA prepares new tariffs
No date yet for the previously announced retaliatory tariffs on $16 billion in US goods, which will largely target commodities. In April, the administration had announced plans to slap tariffs on 1,333 Chinese product lines worth $50 billion a year.
Paul, a member of the Senate Foreign Relations Committee, has continued to meet with Russian officials in Moscow this week along with visiting the USA embassy. He also held talks in Moscow with parliamentarians and pledged to block new sanctions against Russian Federation.
The two countries are also at odds over Syria and Ukraine.
Oil and gas. In the energy sector, the legislation would impose sanctions on investment in any projects by the Russian government or government-affiliated companies outside Russia worth more than $250 million.
A reported text of the draft bill published Wednesday sent Russia's ruble to lows against the dollar last seen in April.
Chinese state media slams Trump for 'extortion'
In a statement , the Commerce Ministry said China could add duties of 5, 10, 20 or 25 percent on 5,207 types of USA imports. Chinese officials are trying to reassure markets and the local population that the USA moves would have little impact.