One mortar shell has hit a building of the US embassy compound in the Liberian capital, Monrovia.
Thousands of people have fled the fighting
There are no reports of injuries from that attack, but more than 60 are being reported killed in less than an hour of bombardment on the centre of the city.
Mortars were fired near the centre of the city after a lull of about 12 hours in fighting between government forces and rebels.
Earlier about 40 US soldiers arrived in the capital to reinforce security at the embassy.
The BBC correspondent in Monrovia says the city streets were crowded with people trying to find food and water during the relative calm when the attack began.
The mortars are coming in rapid succession from the general direction of the port area where fighting is taking place.
Hundreds have taken shelter in United Nations buildings.
Liberians United for Reconciliation and Democracy (Lurd) leader Sekou Damateh Conneh on the BBC's Focus on Africa programme denied that they were shelling the centre of the city.
The continuing fighting is hampering humanitarian efforts to help injured and displaced civilians.
Doctors at two makeshift hospitals run by Medecins Sans Frontieres (MSF) say the recent shooting and mortar bombardment between government militias and rebel troops have made it nearly impossible to treat patients.
Aid agencies say their staff have been trapped indoors by the fighting and are unable to reach centres where thousands of people have gathered and are now living in appalling conditions.
The US soldiers arrived at the embassy by helicopter from nearby Sierra Leone earlier on Monday.
They are there to protect their own staff and people, but not to get involved in the battle that is taking place for the city between government troops and rebels.
Liberians have expressed frustration that the Americans should be sending troops just to protect their embassy.
One man told the BBC that if they are going to come here, they should come to help and stop the breakdown of the ceasefire that was in place.
"A lot of us are dying," he said.
There has also been widespread looting in government-held areas of Monrovia, with gunfire being heard and government militia targeting homes, businesses and vehicles.
Washington has called for an immediate ceasefire.
Over the weekend, the rebels, tried to advance on central Monrovia on two fronts, sending more residents fleeing with their possessions.
By Monday, the rebels were occupying the main port area but government troops had stopped their advance and were in control of two key bridges.
Hospital staff were trying to treat up to 80 civilians severely wounded in the fighting.
Monrovia is a city under siege
The head of the MSF mission in Monrovia, Alain Kassa, said the intense fighting on Sunday made it difficult to transport the injured to hospital for treatment.
"Shooting and shelling close to our hospitals is making it nearly impossible for us to treat our patients safely," he said.
"Yesterday a bullet landed in the middle of our hospital's paediatric ward even as war wounded civilians continued to arrive."
A spokeswoman for Oxfam told BBC News Online that their staff in Monrovia had been unable to carry out their work providing clean water and toilet facilities for displaced people.
She said the conditions in the sports stadium and Masonic lodge where tens of thousands of people had gathered were revolting, with maggot infestations and acute risk of disease outbreaks.
Mr Taylor has accepted an offer of asylum from Nigeria - but he refuses to stand down before the arrival of international peacekeepers.
Nigeria has sent a small number of troops to Liberia to prepare the way for the eventual deployment of a larger West African peacekeeping force.
A Nigerian army spokesman said the job of the advance party was to carry out reconnaissance.
A United Nations envoy has said the US will not take a decision on whether to send troops into Liberia until a West African force is in place.