He apologised for Wednesday's attack on the French embassy by protesters who accused France of abandoning them.
French President Francois Hollande has already said France will not intervene in its former colony.
The UN is evacuating its non-essential staff from the country, while the US has urged its nationals to leave.
There is a mood of deep anxiety in Bangui, and residents are "petrified as to what could happen", the UN envoy in the CAR, Margaret Vogta, said.
The BBC's Junior Lingangue reports from the city that people have been stockpiling food amid fears that the rebels - known as the Seleka coalition - could launch an assault in the next few days.
On Sunday, the rebels captured the northern city of Bambari, the third largest in the country, having earlier seized the rich diamond mining area around Bria.
It is unclear how far they have advanced towards Bangui, but an unconfirmed report by Reuters news agency on Wednesday quoted sources as saying they were only 75km (47 miles) away.
Several thousand supporters marched through Bangui on Thursday to protest against the rebel advance.
"We ask our French cousins and the United States of America, the great powers, to help us to push back the rebels," Mr Bozize told the crowd.
A halt to the rebel advance would open the way for talks to end the conflict, he said.
"There is no question of allowing [the rebels] to kill Central Africans, of letting them destroy houses and pillage, and holding a knife to our throats to demand dialogue," Mr Bozize was quoted by the AFP news agency as saying.
Our correspondent says Mr Bozize also apologised for the protest outside the French embassy, when an angry crowd threw stones at the building and tore down the French flag.
The crowd accused France of abandoning them by refusing to help quash the rebellion.
France has about 200 soldiers based in the CAR and stepped up security at its embassy after the attack.
However, Mr Hollande said France would not intervene military.
"If we have a presence, it's not to protect a regime, it's to protect our nationals and our interests and in no way to intervene in the internal business of a country, in this case the Central African Republic," he said. "Those days are over."
A spokesman for the French foreign ministry told Reuters that the crisis needed to be resolved through dialogue.
Seleka, which is made up of breakaway factions from three former armed groups, accuses Mr Bozize of failing to honour a 2007 peace deal, under which fighters who laid down their arms were meant to be paid.
The rebels have pledged to depose Mr Bozize unless he negotiates with them.
They began their campaign a month ago and have taken several towns in their push towards the capital.
The CAR's minister of territory administration told the BBC the rebels were "engaging in double speak" as they had not respected a call by regional powers for a ceasefire to allow for dialogue.
"The international community must look out for constitutional order. Our president must be able to finish his mandate which ends in 2016," Josue Binoua told the BBC's Newsday programme.
Mr Bozize, who seized power in a coup in 2003 and won two subsequent elections, has repeatedly relied on foreign intervention to fend off rebellions and the spill-over from conflicts in neighbouring Chad and Sudan.
Chad has deployed 150 soldiers to try to stem the rebel advance.
A 400-strong regional peace force, funded by the European Union, which has a mandate to protect civilians is also stationed in the country.