The US leader has been dogged by accusations that Kremlin backed hackers aided his campaign to win the White House.
But after leaving the G20 summit in the German city of Hamburg, Mr Trump tweeted: "I strongly pressed President Putin twice about Russian meddling in our election. He vehemently denied it. I've already given my opinion..."
The first face to face meeting between Mr Trump and Mr Putin was a highly anticipated moment of the summit as the leaders of the world's largest economies gathered in Germany.
The pair had been scheduled to meet for half-an-hour, but ended up talking for over two-hours.
In the end Mr Trump's wife Melania was sent in to end the meeting, but she was unable to stop the pair from talking for another hour, US Secretary of State Rex Tillerson said.
Despite US intelligence agencies having repeatedly said evidence showed Russia interfered in the election, Mr Trump has refused to blame Russia.
Pressed on the issue during a press conference in Poland, Mr Trump said that "nobody really knows for sure" who interfered in the 2016 election, adding: "I think it was Russia and I think it could have been other people countries."
While President Trump continues to doubt whether Russia acted alone in its efforts to influence the presidential race, US intelligence agencies have agreed Mr Putin directed the cyber attacks.
The Russian leader has always denied the claims and it came as no surprise he kept the same line during his meeting with Mr Trump.
Her told reporters after the meeting that Mr Trump had accepted his strong denials of the accusations.
Writing on Twitter, Mr Trump added: "Putin and I discussed forming an impenetrable Cyber Security unit so that election hacking and many other negative things will be guarded...and safe. Questions were asked about why the CIA & FBI had to ask the DNC 13 times for their server and were rejected, still don't have it.
He added: "Fake News said 17 intel agencies when actually 4 (had to apologise). Why did Obama did nothing when he had info before election?"
The Central Intelligence Agency, the National Security Agency, the FBI and the Office of the Director of National Intelligence wrote in a report published in January they had "high confidence" Russian spies had tried to interfere in the election on the order of President Putin.
Not all 17 intelligence agencies were working on investigating interference in last' years US election, but the four that were concluded the same thing.
The US ambassador to the United Nations, Nikki Haley, offered a much more forceful view of the meeting with Mr Putin.
In an interview with CNN, she said: “[Mr Trump] wanted him to basically look him in the eye, let him know that yes, we know you meddled in our elections. Yes we know you did it, cut it out. And I think President Putin did exactly what we thought he would do, which is deny it. This is Russia trying to save face. And they can’t. They can’t.”
She added: "Everybody knows that Russia meddled in our election. Everybody knows that they're mot just meddling in the United States' election."
About his meeting with Mr Putin, Mr Trump also tweeted: "We negotiated a ceasefire in parts of Syria which will save lives. Now is time to move forward in working constructively with Russia!
"Sanctions were not discussed at my meeting with President Putin. Nothing will be done until Ukrainian & Syrian problems are solved!"
From his time in Hamburg, Mr Trump concluded: "G20 summit was a great success for the US. Explained that the US must fix the many bad trade deals it has made. Will get it done!"
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