The claim by rebel spokesman Eric Massi came after a regional stabilisation force commander said explosions and gunfire were heard on the outskirts of the city.
Fighters from the Seleka rebel coalition this week pushed their way to the gates of Bangui following the collapse of a two-month-old peace deal in the country that has been plagued by instability since its independence from France in 1960.
Central Africa’s prime minister earlier Saturday called for talks with the rebels to “avoid a blood bath”.
That call appeared to have gone unheeded, with the rebels later claiming they had passed through a key checkpoint that marks the entrance to the city.
“We call on the population to stay at home, on the FACA (Central African Armed Forces) not to fight, and on President (Francois) Bozize to leave,” said Paris-based rebel spokesman Massi.
News of the rebel advance emptied the streets of Bangui and led many to try and flee the city, locals said.
Massi said the rebel leadership was urging its forces on the ground to refrain from “looting or score-settling with the local population”.
Seleka has said it was open to negotiations with African leaders to resolve the crisis, which has sparked concern at the UN Security Council, but rejected any talks with Bozize.
“If the heads of state of the Economic Community of Central African States request it, we are ready to meet them and talk, but not to negotiate with General Bozize,” Djouma Narkoyo, a rebel military chief, told AFP by telephone.
“How many times have we talked with him? It never leads to anything.”
He added that if the rebel coalition managed to take Bangui, it would set up a new government.
Seleka, an alliance of three rebel movements, first launched an offensive on December 10 in the north of the country, accusing Bozize of not abiding by the terms of previous peace agreements.
Facing little resistance from an ill-trained and ill-equipped army, they seized a string of towns, defying UN calls to stop, before halting within striking distance of Bangui.
They reached a peace deal with the government in early January under which Nicolas Tiangaye, an opposition member, became head of a national unity government that was to carry out reforms before national elections next year.
But the fragile deal soon collapsed, with rebels saying their demands — such as the release of political prisoners — had not been met.
Last weekend, Seleka rebels detained five ministers from the new government — including members of the rebel coalition — to back their demands for concessions from the authorities.
Bozize then offered to release political prisoners and end a night-time curfew in a bid to head off a showdown with the rebels, but Seleka said this was not enough.
Rebel military chief Narkoyo also called for South African troops — which were deployed in the country at Bozize’s request after Seleka’s lightning advance in December — to leave.
The international community has nervously watched the spike in tensions in the country, a landlocked nation of 4.4 million people where Bozize seized power in a 2003 coup.
The chief prosecutor at the International Criminal Court has warned that her office would investigate and prosecute anyone alleged to have committed crimes in the conflict.