"I don't see any fundamental change," Mr Perry told reporters travelling with him on a three-day visit to Russia.
The Defense Secretary was discussing his testimony earlier in the day before the Russian lower house of parliament, the Duma, on the Start II arms reduction treaty. He was to have met Mr Lebed last night, but he said US officials decided it was "unwise" to go ahead with the meeting.
In Washington, the Clinton administration responded calmly to the Russian security chief's firing. "We consider this a Russian internal political matter," a White House official said, speaking on condition of anonymity. "President [Boris] Yeltsin is the elected president and has taken a step which is clearly within his constitutional prerogatives."
Asked about charges of coup-plotting against Mr Lebed made by another member of Mr Yeltsin's government on Wednesday, Mr Perry replied:"I think those were overblown."
"Our security relationship will proceed as it has been proceeding," Mr Perry said. "It is strong and growing."
The Defense Secretary said US officials "had never really had a chance" to get to know Mr Lebed very well. He noted that the ailing Mr Yeltsin is waiting to undergo surgery in November "and all our best wishes will be with him".
"We should not be surprised that there are problems as Russia emerges as a democratic state," he said. "We should be happy that they are handling those problems effectively. Any student of history that studies the first 10 years of the American emergence as a democratic nation will discover that there was a hell of a lot of turbulence in those first 10 years."
But the US Ambassador to the Soviet Union, Thomas Pickering, who also attended the session, posed the question: "Is Lebed still a major political force? That's a question to watch." Mr Pickering said that Mr Lebed's departure may leave a political vacuum. Mr Lebed is "a considerable force in Russian politics ... [but] Yeltsin has made clear, when it comes to the crunch, he will act", Mr Pickering said.
Earlier, Mr Perry appealed to Russian politicians to approve the sweeping Start II arms reduction treaty. But his audience reacted with suspicion and distrust of US intentions, particularly Washington's support for Nato expansion. "I believe the Start II treaty is fair and gives neither side an advantage. Both of us know that fewer nuclear weapons in the world makes us all safer," Mr Perry said.
Lev Rokhlin, chairman of the Duma defence committee, told Mr Perry: "Ratification of Start 11 is quite problematic, it is not in the interest of the Russian side." Mr Perry had testified that each nation could save nearly $5bn over five years by destroying warheads instead of maintaining huge arsenals.
"Russians are disappointed with tendencies emerging in America, and it would be difficult to convince the Russian public that the United States is friendly and has peaceful intentions towards Russia." Vladimir Lukin, chairman of the Duma's international committee, said after the meeting.