"To simply say every country should have the right to apply to any alliance it wants, that's true. But an alliance and its members should also have the right to determine whether it's in their interests to take in a member," Matlock told a forum sponsored by the Carnegie Endowment for International Peace.
"I'm saying it's not in the United States' interests, and it's not in NATO's interests," said Matlock, who was ambassador to Moscow from 1987 to 1991.
President George W. Bush firmly backs Georgia and Ukraine in NATO.
Georgia had not settled territorial disputes with its neighbors and appeared to want to use NATO to help resolve them, Matlock said, in a reference to last month's war with Russia.
As for Ukraine, joining NATO would risk splitting a country where many people oppose the bid, he said.
He said genuine strategic cooperation with Moscow would be nearly impossible "as long as we're pushing this."
Matlock and former U.S. Ambassadors James Collins and Arthur Hartman shared a platform with two former Soviet ambassadors to Washington, Alexander Bessmertnykh and Yury Dubinin, who denounced the NATO expansion policy as a major irritant in relations. "I personally believe that we need to go slow. ... If we don't, we will find that this is not something that stabilizes but rather divides," Collins said.
Hartman said it was a "great failure" that the West did not think creatively about a structure to replace NATO when the Soviet Union collapsed because the main purpose of its existence, to defend against a Soviet threat, no longer existed.
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