At a gathering of five former U.S. and Russian ambassadors, Matlock questioned a central tenet of Bush administration policy: its firm support for the NATO membership bids of both Georgia and Ukraine.
Some European countries have doubts about the policy, and some U.S. analysts have blamed it for helping provoke the brief war last month between Russia and Georgia over the breakaway region of South Ossetia.
Since Russian troops crushed Georgian forces in that conflict, U.S. ties with Moscow have plummeted
"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 the forum in Washington, 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 under former President George H.W. Bush and his predecessor, Ronald Reagan.
Georgia had not settled territorial disputes with its neighbors, and appeared to want to use the NATO military alliance to help resolve them, Matlock said, in a reference to its conflict with Russia.
As for Ukraine, which like Georgia is a former Soviet republic, most of its population opposed membership and joining NATO would risk splitting the country, Matlock said.
He added that genuine strategic cooperation with Moscow, which vehemently opposes NATO membership for the two former Soviet republics, would be nearly impossible "as long as we're pushing this."
U.S. Secretary of State Condoleezza Rice met Georgian President Mikheil Saakashvili in New York on September 23 on the sidelines of the United Nations General Assembly. A day earlier, she met Ukraine's foreign minister and pledged Washington's firm support for Ukraine's bid to join NATO.
But in Washington, Matlock and former U.S. envoys to Moscow James Collins and Arthur Hartman pointed to the consequences of ignoring Russia's attitude on NATO expansion.
They shared a platform with two former Soviet ambassadors to Washington, Aleksandr 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 that at the time the Soviet Union was collapsing in the early 1990s, it was a "great failure" that the West didn't think creatively about a structure to replace NATO -- because the main purpose of its existence, to defend against a Soviet threat, no longer existed.