"America needs its own perestroika," the former Soviet leader said Thursday.
With the overwhelming election of Obama, "the entire world felt that America wanted change and was expecting change," said Gorbachev, 77.
Obama's detractors in Russia express hope that his policies will lead to the demise of the United States, pointing to the collapse of the Soviet Union in 1991 following Gorbachev's liberal reforms.
But Gorbachev said the world needs a strong United States, as shown by the current global financial crisis, and he urged Washington to use its power for the good of all.
"America is needed -- an America that is strong, democratic and sure of itself -- for the entire world, not just for Americans," he said. "We are seeing that if it's bad for America, it's bad for us all."
He said many world leaders, including those in Russia and Iran, are eager for improved relations with Washington, and he urged Obama not to miss the opportunity.
For many Americans, Russia has moved to the top of the list of rogue nations, Gorbachev said. He expressed hope that Obama would usher in a new period in Russian-U.S. relations when he becomes president in January.
When most world leaders were extending congratulations to Obama on his victory, President Dmitry Medvedev threatened to station short-range missiles in Kaliningrad if the United States pushed ahead with missile-defense sites in Eastern Europe.
Gorbachev said it was not an attempt to test the young president-elect.
"This was simply something from a past era," he said. "As you do to us, we will do to you. ... We don't need this."
He urged Obama to "muster his courage" and reconsider the decision to station missile-defense sites in Poland and the Czech Republic.
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