Mr Zuckerberg said the exchange occurred during past discussions the men have had.
"I have had certain discussions with him in the past and where I've told him that I thought some of the rhetoric was problematic," Mr Zuckerberg said. "If I did talk to him, you know, be clear about how - just the importance of making sure that people have confidence in the election."
On Thursday, Facebook announced new measures to prevent election interference in the 2020 US election.
Mr Zuckerberg said the policies would apply to Mr Trump as well. The president has formerly had his posts fact checked and flagged for containing misleading or incorrect information.
"This will definitely apply to the president once this policy goes into place, and it will apply to everyone equally," he said.
Under the new policies, Facebook will ban any new political advertisements from the platform in the week prior to the election. Existing ads will still be played on the platform, however.
"We're going to block new political and issue ads during the final week of the campaign," Mr Zuckerberg wrote in a Facebook post. "It's important that campaigns can run get out the vote campaigns, and I generally believe the best antidote to bad speech is more speech, but in the final days of an election there may not be enough time to contest new claims."
Mr Zuckerberg has long opposed the argument that Facebook should be regarded as a publisher and be held to the same standards as newspapers and digital news outlets, but the new policies appear to indicate a shift in his thinking.
"This election is not going to be business as usual," he said. "We all have a responsibility to protect our democracy."
Mr Trump was is not pleased with the changes, and lashed out after the announcement.
"When millions of voters will be making their decisions, the president will be silenced by the Silicon Valley Mafia," a spokesperson for the Trump campaign said.
Some Democrats appeared opposed to the move as well. Acronym, a digital group allied with the Democrats, said the move was a decision to "tip the scales of the election tot hose with the greatest followings on Facebook, and that includes President Trump and the right-wing media that serves him."
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