Trump and Putin shook hands Friday at the Asia-Pacific Economic Cooperation (APEC) summit in Danang, Vietnam, but they will not have a scheduled, formal sit-down.
"The Russians really wanted this formal sit-down meeting behind closed doors," Peters said on "America's Newsroom." "Vladimir Putin thinks in historical terms. In the Great Patriotic War - which we call World War II - the big three were Churchill, Roosevelt and Stalin. Today, in Putin's view, the big three are Trump, [Chinese President] Xi and Putin."
He said that Putin didn't want to appear slighted after Trump's two-day meeting with Xi in Beijing.
"Fortunately, it appears that Trump's senior staff members realized that the optics of a closed-door meeting with Vladimir Putin right now would be very bad for President Trump," Peters said. "So, smart for President Trump."
He added that this hurts Putin, who wants to be seen as important and legitimate on the international stage.
"President Trump, I'm very glad that listened to his advisers and has ducked the formal meeting," Peters said. "The important thing is for us not to give Putin credibility he hasn't earned."