Washington (CNN) The former Director of the National Security Agency, retired Admiral Mike Rogers, said Tuesday that he thought President Donald Trump should have taken the opportunity to confront Russian President Vladimir Putin publicly in Helsinki, Finland over Russia's election meddling.

"I thought there was an opportunity there that I wish we would have taken advantage of," Rogers said at an event at George Mason University in Arlington, Virginia, on the relationship between the presidency and the intelligence community.

In July, Trump met one-on-one with Putin, a meeting he did not ask his top intelligence officials -- including Director of National Intelligence Dan Coats -- for advice on, Coats later revealed.

During a press conference with the Russian leader, Trump undermined the US intelligence community's universal conclusion that Russia had made attempts to attack the 2016 US presidential election, through digital interference and other methods.

'A different direction'

"My people came to me, Dan Coats came to me and some others, and said they think it's Russia," Trump said. "I have President Putin. He just said it's not Russia. I will say this. I don't see any reason why it would be, but I really do want to see the server."

Press secretary Sarah Sanders later clarified Trump meant to say he had no reason to believe it "wouldn't" be Russia, using the wrong word — but at that point, the damage of the remarks and the skepticism he expressed had already led to bipartisan outcry, particularly as intelligence officials warn that Russia may continue to attempt to attack US elections as the midterms approach in November.

Speaking at George Mason University, Rogers went on to say that Trump "opted to go in a different direction and that certainly is his right as the President," adding, "but I wish we had taken advantage of that opportunity."

The former NSA chief said a public push back "could have sent a very powerful message."

In the discussion on Tuesday evening, Rogers also recounted his conversations with Trump about Russia's continued attempts to disrupt the US electoral system through cyber means in 2016 and beyond.

"He would often say to me, 'Mike you know I'm in a different place on this,' I said, 'Mr. President I understand that, but you pay me, I am paid by the citizens of the nation to tell you what we think. Sir, this isn't about politics, it's not about parties, this is about a foreign state that is attempting to subvert the very tenets of our structure, that is trying to undermine us. That should concern us all as citizens, that should concern us as leaders and if we don't do something they are not going to stop.' "

Rogers and the other senior intelligence officials working for both Trump and Obama have routinely affirmed the intelligence community's January 2017 declassified assessment that the senior-most echelons of the Kremlin were behind aggressive attempts to sow chaos and damage trust in elections, with the aim of electing Trump.

Rogers also sought to correct previous media reports that Trump had told him to publicly state that there was no collusion between Russia and the Trump campaign in the 2016 election.

"I have never had a discussion on collusion," with Trump or members of his senior staff, Rogers said. "I have never been directed to do anything, coerced, anytime I had a discussion, I felt I was able to say here is my view on that, I am very comfortable with it."

Rogers also talked about his decision not to sign the letter from hundreds of former national security officials protesting Trump's decision to take away former CIA Director John Brennan's security clearance.

"I said to myself, is this gonna be productive? So a group of former senior intelligence individuals complaining about how another former senior intelligence official is being treated, I'm not sure that's the most effective way to address a very valid concern," Rogers said.

Rogers said he thought that "pouring gasoline on the fire is not gonna reduce the flame. And we got enough fires burning right now. We need to focus on what are the outcomes we need to achieve as a nation."

"I agree with the point the letter is making," Rogers added, "but I'm concerned that it isn't the most effective way to make the point. And number two, I'm concerned about what this will do for the men and women who are doing the work in the agencies that we have all been a part of, and as a result I opted not to go this route even as I recognized, john, everybody, you need to speak up and say what you believe. I don't question that for one minute."

This story has been updated to correctly reflect the location of the George Mason University campus where Mike Rogers spoke.