Bangui has been unstable for many years
Residents in the capital reported seeing a plane-load of Libyan troops and equipment arrive at Bangui airport.
Libyan soliders and members of the presidential guard have been protecting President Ange-Felix Patasse in his residence, while troops loyal to a sacked army chief, General Francois Bozize have set up roadblocks in the north of the capital.
Gunfire was reported for the third day.
Mortars were reported to have been fired at President Ange-Felix Patasse's villa from a hill overlooking the city in the early hours of Monday but failed to hit their target.
Shots were then heard mid-morning near the villa, which is in the centre of the city.
A correspondent for the BBC in Bangui says Libyan troops - who form the last line of defence for the president - have also been involved in the fighting against bodyguards of General Francois Bozize, who was sacked last month.
No official details have emerged about casualties but residents have been fleeing the city to escape the fighting.
Meanwhile, negotiations lead by the United Nations representative in Bangui, the Senegalese General Lamine Cisse, are continuing to try to resolve the military standoff.
Libya
The Libyans intervened in the central African Republic in May when a former military ruler tried to overthrow the elected civilian president.
This latest crisis began late last month after the army chief of staff was accused of being part of the coup attempt in May.
General Bozize denies this and says that in fact he played a key role in defending President Patasse by putting the coup down.
When President Patasse's troops moved on Saturday in an apparent attempt to arrest General Bozize, shooting started and military road blocks went up around the houses of both men.
Instability
General Bozize's men, drawn from part of the army loyal to him, are reported to have moved from his home area in the north of the city and to have crossed a key bridge that leads towards the centre of town.
The United Nations used to have a peacekeeping force in the Central African Republic.
But now there is just a political presence.
Mr Patasse' election in 1993 ended a long period of military rule.
The Central African Republic has seen numerous military coups and revolts since independence from France in 1960.
The French used to maintain a military garrisson there to protect their interests, but it often became embroiled in local politics.
When the French withdrew, the UN briefly tried its hand at enforcing peace.
But when the UN force was itself subsequently scaled down, the Central African Republic's bitter ethnic and political disputes blew up once again.
Now the Libyans are playing a role they say is aimed at encouraging stability.
But none of these foreign forces has succeeded in providing the secure environment ordinary Central African citizens need.