Trump has faced criticism from both Democrats and Republicans about his handling of the Helsinki summit with Putin on Monday.
The White House hasn't commented yet on the allegation but in a series of tweets in the hours after publication, Trump once again slammed the news media over the Russian Federation summit as the "enemy of the people".
"My people came to me, Dan Coats came to me and some others, they said they think it's Russian Federation". He says with that pressure on him, why shouldn't the USA go forward and see what happens. "Hopefully President Putin will have the 12 identified Russians come to the United States to prove their innocence or guilt".
"For us right now, it's kind of steady as she goes".
Critics have accused him of siding with Russian Federation over his own country by failing to criticise Moscow for what USA intelligence agencies a year ago described as Moscow's interference in the 2016 election in an attempt to sow discord, aid Trump's candidacy and disparage Trump's Democratic opponent Hillary Clinton.
Antonov also said that Trump and Putin may work together on joint military operations against terrorism in Syria.
White House spokeswoman Sarah Sanders said that meeting may come this fall.
Russia's official assessment of Trump's high-stakes summit with Putin is carefully upbeat.
"Say that again?" Coats asked the interviewer. The two presidents met for over two hours one-on-one, with only translators, meaning that no written record of what was discussed exists. They also chanted 'we the people say you are fired, ' using his line from when he was host of the TV show "The Apprentice".
The talks in the Finnish capital were closed-door and with no one else present but interpreters.
'It seemed to me, my impression was that the USA side listened ... with interest, ' Antonov said. "In a key sentence in my remarks I said the word "would" instead of "wouldn't", a back-pedaling Trump told reporters.
It came as USA intelligence chief Dan Coats said Russian Federation was involved in "ongoing, pervasive efforts to undermine our democracy".
The White House later said the USA president had been saying "no" to further questions from reporters and that the threat to the U.S. electoral system "still exists".
Putin did not name names, but spoke of USA politicians who put their "narrow party interests" above the best interests of the United States and were powerful enough to be able to foist their questionable "stories" on millions of Americans.
Sen. Lindsey Graham says Trump's had a "bad week" when it comes to Russian Federation in the wake of the Trump-Putin summit Monday in Helsinki.
Former Secretary of State Madeleine Albright on Thursday slammed the White House for considering a Russian proposal to interrogate Americans in exchange for assistance in the Mueller investigation.
Putin had both good and bad things to say about Trump in a broad speech about foreign policy.
According to opinion polls published Thursday, a large majority of Americans disapproved of Trump's handling of the summit - but members of his party approved by a wide margin.