(CNN) We might never know exactly what they discussed -- nor can either side now seem to agree -- but President Donald Trump emerged fresh with optimism on Friday after a first face-to-face meeting with Russian counterpart Vladimir Putin.

Speaking to reporters after the sit-down, Secretary of State Rex Tillerson remarked on Trump's and Putin's easy comfort.

"The two leaders, I would say, connected very quickly," he said. "There was a very clear positive chemistry between the two."

Tillerson, who knows Putin well from his time dealing with Moscow as the CEO of oil giant ExxonMobil, added that the conversation didn't include much "relitigating of the past."

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Trump's relationship with Putin and their personal interactions in Hamburg were always going to come under some scrutiny. The Russian government's meddling in the 2016 presidential election has been a source of constant strain for Trump, and enduring frustration for his political rivals. The irony here is less that the two men seem to have gotten along and more that early reviews of the meeting feel weirdly familiar.

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