"The president of the republic will carry on guaranteeing the continuity of the state ... until elections are held," Gbagbo said in a broadcast to the nation.
"I will never allow the decapitation of the state of Ivory Coast," he added, rejecting demands by political foes and armed rebels in control of the north of the country since a 2002 civil war that had split the world's No 1 cocoa grower in two.
Earlier, soldiers and riot police in the country's main commercial city Abidjan fired warning shots and tear gas to force opposition supporters marching towards the presidential palace to turn back.
Several people were reported injured, but it was not clear how seriously, UN sources said.
Several hundred protesters took to the streets and set piles of rubbish on fire after attending a big anti-Gbagbo rally. They scattered when soldiers and police fired automatic rifles into the air and launched tear gas.
Gbagbo, who said he was acting according to the constitution, blamed his opponents for the fact that elections originally scheduled to be held on Sunday were not taking place.
The opposition has threatened to
force Gbagbo out through protests
The Ivorian president said the rebels, who have warned they will not recognise him as president after Sunday, had failed to disarm and unify the country in line with internationally brokered peace efforts.
Gbagbo said he would seek to implement a recent UN resolution that foresees him staying on for up to 12 months more until elections are held, and also calls for the appointment of a strong prime minister acceptable to all sides.
"I hope elections will take place well before 12 months ... that is a job I will entrust to my new prime minister whom we will name in a few days," Gbagbo said.
A UN source said Nigerian President and African Union chairman Olusegun Obasanjo was expected in Abidjan early next week to lend his support to the UN peace plan.
At the anti-government rallies in Abidjan and the rebel-held north, opposition youth leaders repeated threats to force Gbagbo out with street protests.
"At midnight, Gbagbo is no longer president. In a few hours, we are going to take power," Jean Ble Guirao, an opposition
youth leader, told the Abidjan rally.
"I will never allow the decapitation of the state of Ivory Coast"
Ivory Coast President Laurent Gbagbo
The authorities had banned any protest that was not confined within an enclosed area.
The army reinforced security around the presidential palace, deploying extra patrols and several armoured cars.
Opposition and rebel leaders have rejected the UN formula keeping Gbagbo in office. They insist the new prime minister should come from their ranks.
In a symbolic gesture of defiance, the rebel New Forces named their leader, Guillaume Soro, as prime minister of what they called a future government of national reconciliation, according to a rebel statement sent to Reuters.
Soro said he would announce members of his cabinet shortly, it added.
In a statement, UN Secretary-General Kofi Annan urged Ivorians to keep working for peace.
Soldiers fired warning shots and
tear gas at protesters in Abidjan
"I call on all the Ivorian parties and their followers to refrain from any actions that might create tensions and to remain committed to the ongoing peace process aimed at restoring lasting peace and stability to their country," he said.
The standoff in the Ivory Coast has raised fears of renewed violence in the former French colony, which has suffered riots, massacres and looting in the last few years.
As police and soldiers pushed the Abidjan protesters back, officers slapped and manhandled a Reuters reporter at the scene, taking his cellphone and tearing up his notebook. He was later allowed to leave unharmed.