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President Biden said the tone of his highly-anticipated meeting with Russian President Putin was "good" and "positive," saying he made "no threats" to his Russian counterpart, but warned of "consequences."

Biden, on Wednesday, reflected on the hours-long meeting with Putin, saying "there was a lot of hype" around it, but said the meeting was "straightforward." 

"There is no substitute for face-to-face dialogue between leaders. None," Biden said, noting that he and Putin "share a unique responsibility to manage the relationship between two powerful and proud countries." 

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The president maintained that the U.S. relationship with Russia "has to be stable and predictable," and said the countries "should be able to cooperate where it is in our mutual interest." 

"We have differences, where I want Putin to understand why I say what I say, and why I do what I do, and how I will respond," Biden said. "My agenda is not against Russia, or anyone else. It is for the American people—fighting COVID, rebuilding our economy, reestablishing relationships around the world with our allies and friends and protecting the American people." 

Biden said the meeting was "good, positive," and their discussion was "not done in a hyperbolic atmosphere." 

"This is about how we move from here," Biden said. "This is about practical, straightforward, no-nonsense decisions that we have to make, or not make." 

But Biden maintained that the relationship with Russia is "not about trust," but "self-interest and verification of self-interest." 

"There were no threats," Biden said. "It was very, as we say, which will shock you coming from me, somewhat colloquial." 

"There were no threats, just simple assertions made," Biden continued. "It was just letting him know where I stood, what I thought we could accomplish together, and what, in fact, if there is violations of American sovereignty, what we would do." 

He added: "I know we make foreign policy to be this great, great skill—but it is just a logical extension of personal relationships. It is the way human nature functions." 

Biden went on to say that he "doesn’t think Putin is looking for a Cold War with the United States." 

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"This is not a Kumbaya moment," Biden said. "But it is clearly not in anybody’s interest, yours or mine, to be in a situation where we’re in a new Cold War." 

The president said that in the coming months, the U.S. will "find out" whether there is a "strategic dialogue" with Russia and whether there is a "cybersecurity arrangement that begins to bring some order." 

Biden said the two leaders spoke about human rights abuses, saying that he made clear to Putin that no president of the United States "could keep faith with the American people if they did not stand up for universal and fundamental freedoms that all men and women have." 

Biden said that "consequences of that would be devastating for Russia" if jailed Russian opposition figure Alexei Navalny dies in prison. 

"The bottom line is, I told Putin we have to have some basic rules of the road we can all abide by," Biden said, adding that it is in "our mutual interest, for our people—Russian and American people—but also for the benefit of the world, the security of the world." 

Biden said he also discussed strategic stability with Putin, and addressed next steps in arms control to "prevent unintended" conflict. Biden also announced that they launched a "bilateral strategic stability dialogue" with military experts and diplomats to "work on a mechanism to lead to control the new and dangerous sophisticated weapons that are coming on the scene now that raise the prospects of accidental war." 

The president also said the two discussed cybersecurity, telling Putin that "certain critical infrastructure should be off limits to attack." Biden said he gave a list of "16 specific entities defined as critical infrastructure," saying it ranges from energy to water systems. 

Biden, though, said they "didn’t talk about a military response" should Russian actors attack U.S.-based infrastructure. 

The latest ransomware assault took place earlier this month, shutting down the U.S.-based meat plants of the world's largest meatpacker, Brazil-based JBS. The White House said the hack was carried out by a criminal group likely based in Russia. 

That attack came just weeks after the largest U.S. fuel pipeline, the East Coast’s Colonial Pipeline, was targeted by a criminal group originating in Russia. 

Another issue that came up in Biden and Putin's meeting: the string of directed-energy microwave incidents targeting U.S. diplomats and top national security and CIA officials, a senior administration official told Fox News. The attacks, first noticed in Cuba and later reported in Moscow, Shanghai and Washington, D.C., have become known as the "Havana Syndrome."

Putin, during his press conference after the meeting, denied that Russia was responsible for cyberattacks, instead claiming that the most cyberattacks in the world were carried out from the U.S.

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"Responsible countries need to take action against criminals who conduct ransomware activities on their territories," Biden said, adding that the leaders tasked experts "in both countries to work on specific understandings about what is off limits." 

As for the Middle East, Biden said Putin agreed to work with the U.S. to "ensure that Iran does not acquire nuclear weapons," saying that "it is as much in Russia’s interests as ours." Biden also said they discussed the need to "prevent a resurgence of terrorism in Afghanistan." 

The president also said they discussed the sovereignty to Ukraine. 

"It was important to meet in person so there could be no mistake about, or misrepresentations about, what I wanted to communicate," Biden said. "I did what I came to do." 

Biden again maintained that he "communicated directly that the U.S. will respond" to Russian aggression. 

"I believe, and I hope, the U.S. has shown the world this week that we are back standing with our allies," Biden said, reflecting on his first trip overseas as president, where he participated in the G-7 and NATO summits, along with bilateral meetings with world leaders. 

"We rallied our fellow democracies to make concerted commitments to take on the biggest challenges our world faces," he said. "We’ve gotten a lot of business done on this trip." 

Meanwhile, Putin agreed there was "no hostility." 

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"Quite the contrary," Putin said during the press conference. The Russian leader acknowledged that the two men did not share positions on many issues, but said he felt that "both of these sides showed a willingness to understand one another."

Putin said the talks were "constructive," and said that Russia and the U.S. agreed to conduct negotiations regarding cybersecurity.  

Fox News' Rich Edson contributed to this report.