"Getting along with President Putin, getting along with Russian Federation is a positive, not a negative", Trump said.
Democratic Senate leader Charles Schumer said that unless details of the Helsinki summit are known, the U.S. president should refrain from more one-on-one interactions Putin "in the United States, in Russian Federation, or anywhere else". All we have is a new plan likely to make it all worse with another meeting between Trump and Russian President Vladimir Putin.
The Kremlin has yet to formally respond to the proposal, but Mr Trump has said he is looking forward to his second meeting with Mr Putin. Once he got there, he returned to Twitter to complain about news coverage of Monday's meeting. "In the Old Days they would call it Diplomacy. If I was loud & vicious, I would have been criticized for being too tough".
A White House official said the next Trump-Putin meeting would address national security concerns they discussed in Helsinki, including Russian meddling.
A White House official who spoke on condition of anonymity did not specify if that included Russia's interference in USA elections. Limited details have emerged, but Antonov said discussions included ways to cooperate on arms control and Iran's nuclear activities.More news: Eight injured after knife attack on bus in Germany
Both Trump and Putin earlier on Thursday praised their first meeting as a success and blamed forces in the United States for trying to belittle its achievements.
Secretary of State Mike Pompeo told Voice of America this week that the Russians made proposals on "a number of things" in Helsinki.
"I don't know what happened in that meeting", he said.
I think what's important about that conversation is, it's not that one side is right, one side is wrong.
The White House, with Trump under fierce criticism in the United States, did on Thursday reject Putin's proposal that Russian authorities be present for the questioning of Americans it accuses of "illegal activities", including a former USA ambassador to Moscow.
Hours after Antonov spoke, the White House shot down the idea, saying the Trump administration "is not considering supporting" such a referendum. Such a meeting would be another step towards discussing and resolving problems between the two countries, he said.
Director of National Intelligence Dan Coats said Thursday he had yet to be briefed on the private session.More news: Vivo NEX India Launch
The Russian government has been somewhat more forthcoming. "That's going to be special", he said, after expressing shock at the news. He did not elaborate on what Putin's solutions would be.
The first footage of a live launch of the Avangard hypersonic missile, which Moscow says boasts "a glider manoeuvring warhead", was also aired along with a clip of the heavy Sarmat intercontinental ballistic missile.
Ambassador Anatoly Antonov said Russian Federation "was always open to such proposals" and that Moscow is "ready for discussions on this subject".
However, neither Trump nor the White House has confirmed any agreements between the two countries.
Following their meeting in Finland, Trump tweeted of looking forward to a second meeting with Russia's president: "The Summit with Russian Federation was a great success, except with the real enemy of the people, the Fake News Media".
That happened following Trump and Putin's Finland meeting this week, when Coats had to reiterate the USA intelligence position on Russian meddling in the 2016 election.More news: Alyssa Milano defends Netflix's "Insatiable" against fat-shaming accusations