Their warning came as the head of the African Union preparing to launch peace negotiations.
AU chief Thomas Boni Yayi, president of Benin, is expected to travel to Bangui to try to initiate talks between the government of President Francois Bozize and the rebel coalition known as Seleka.
But a rebel spokesperson told AFP that Bozize's departure should be on the agenda, and that rebel forces have not ruled out entering the capital of the chronically instable country.
"Bozize intends to give battle in Bangui, and if the situation demands it, we will take action," Eric Massi told AFP by telephone from the Gabonese capital Libreville, while reiterating that the rebels were not currently planning to seize the capital.
Tensions were high in Bangui after the country's armed forces, in the face of the rebels' advance, retreated to Damara, the last major town on the way to Bangui, about 75 kilometres, in the southwest.
With the rebels closing in, the Economic Community of Central African States (Eccas), which has troops in the country, warned both sides on Sunday that Damara must remain in government control.
"The Eccas forces are on maximum alert, and the city of Damara is the line not to be crossed. We ask the Faca (government forces) and the rebels not to advance from their current positions and to give talks a chance," said Antonio Di Garcia, head of the regional bloc's mission, on national radio.
The rebels are insisting on the departure of Bozize, who took power in a 2003 coup then won two elections. "That issue must be discussed with the African Union," Massi told AFP.
"President Bozize must recognise his military defeat on the ground ... and draw the necessary conclusions." The rebels, who now control five regional capitals in the centre and north of the country, faced no resistance as they entered the town of Sibut around 150 kilometres from Bangui on Saturday, a military official told AFP.
Officials on both sides said the rebels had also repelled army soldiers trying to recapture Bambari, a former military stronghold in the landlocked country, one of the world's poorest despite vast mineral wealth.
The coalition of three rebel movements known as Seleka – or the "alliance" in the Sango language – launched their offensive on December 10 claiming the government has not fulfilled the terms of peace pacts signed in 2007 and 2011, which include providing for disarmament, pay and social reintegration for insurgents.
No outside support
Bozize's appeals for help from former colonial power France and from the United States to fight the rebels have fallen on deaf ears. Neighbouring Chad, which helped Bozize with rebellions in 2010, has sent a contingent to the country, but those troops too have retreated from the rebel advance.
In Bangui, the population is fearful of a rebel attack and the uncertainty has caused a sharp spike in food prices. "I'm afraid of the rebels coming," said vegetable vendor Euphrasie Ngotanga in the city's huge Sambo market.
"We're not going to sell our produce if there's no peace. And then how we will feed our children?" The Central African Republic is notorious for unrest including coups, army mutinies and rebellions. – Sapa-AFP