Nino Burdzhanadze, who had been an important member of the opposition, appealed to Georgia's people to cooperate and reaffirmed her country's pro-western stance.
"Order must be restored immediately not only in Tbilisi but also in all the regions of the country," she said in a nationally televised speech.
Life in Tbilisi appeared to be returning to normal Monday after a night of street parties, and only a few dozen stragglers stood outside the parliament building, the epicenter of the protests. Traffic flowed freely along Tbilisi's main Rustaveli avenue for the first time in days, with the bustle of a normal work week getting under way.
Shevardnadze resigned Sunday after a decade of mounting discontent and three weeks of protests over Nov. 2 parliamentary elections that his critics said exemplified the corruption that has plagued the former Soviet republic during his reign. The transition has been peaceful so far.
He said he was stepping down to avoid a bloodbath in a region steeped in violence.
"I realized that what is happening may end with spilled blood if I use my rights" to employ force against the protesters, said Shevardnadze, who for weeks had rejected opposition demands that he step down in the wake of the parliamentary vote.
"The president has accomplished a courageous act," said opposition leader Mikhail Saakashvili, head of the National Movement and the loudest voice calling for Shevardnadze's resignation. By the time Shevardnadze did so, some servicemen had joined the protest crowds and it was unclear whether police and soldiers would have obeyed orders to use force.
Burdzhanadze, a scholarly looking 39-year-old lawyer, acted quickly to ensure their loyalty. She convened a meeting of the country's top security officials, including Tedo Dzhaparidze, the security council chairman whom Shevardnadze had fired Sunday after the official publicly acknowledged electoral fraud and called for new elections.
Conspicuously absent was Koba Narchemashvili, the interior minister who had stood by Shevardnadze as he declared a state of emergency Saturday.
In her speech, Burdzhanadze said that because of the rigged elections, the previous parliament — which she chaired — would resume its duties. She said that the constitution required elections in 45 days, and confirmed that balloting for both the president and parliament would be held.
While many Georgians have long detested Shevardnadze for letting corruption infest the country while most of its people fell into poverty, it was the parliamentary elections that galvanized the opposition and started the swell of protest.
The swift denouement to Georgia's deepest political crisis in years came after opposition supporters rushed into parliament Saturday as Shevardnadze tried to convene the legislature his government said was elected in the Nov. 2 vote. The president was hustled out a back door by leather-jacketed bodyguards in a nationally televised scene that began the tense endgame.
On Sunday, Saakashvili issued a resignation ultimatum and said Shevardnadze's residence would be stormed if he didn't comply. As protesters converged on the residence, Saakashvili, another opposition figure and Russian Foreign Minister Igor Ivanov arrived separately. Within about an hour, Shevardnadze's resignation was announced.
When elation over Shevardnadze's resignation fades, Georgia's former opposition leaders will face the grave challenge of maintaining unity and addressing the Caucasus nation's persistent problems.
Georgia, which sits astride a planned oil pipeline between the Caspian Sea and Western customers and is wedged between NATO-member Turkey and Russia, is of substantial strategic interest to both Washington and Moscow, which showed its desire for involvement by sending Ivanov to Tbilisi and has bristled at U.S. military involvement in the nation.
"The change of leadership in Georgia is the natural result of a series of systemic mistakes in the domestic, foreign and economic policy of the nation's former leadership," Russian President Vladimir Putin said during a Cabinet session televised in part by Rossiya state television. "Corruption has increasingly dominated both economics and politics in Georgia. People have stopped seeing any light ahead."
The United States recognized Burdzhanadze as interim president, offering support for Georgia's new leaders while urging them to seek stability, abide by the constitution and hold democratic elections.
The European Union's executive Commission said Shevardnadze's resignation "opens the way to restoration of constitutional law and order" and stressed that democratic elections must be held to help "restore a climate of trust and confidence" in Georgia.
A plane that landed in southern Germany on Monday touched off speculation that Shevardnadze — first known to Americans as the Soviet foreign minister who guided his country through the end of the Cold War — had come to Germany after quitting as Georgia's president, but federal border police said he was not aboard.