Some 3,000 US marines could deploy from warships off the coast
Fighting has broken out despite an appeal from Liberia's interim president, Moses Blah, on his first full day in office for rebels to lay down their weapons and help rebuild the country.
The latest clash involves rebels of the Model group who have advanced to within 30 kilometres of Monrovia's international airport, according to the government.
The government and rebels are blaming each other for the clashes which erupted a day after Liberian President Charles Taylor flew into exile as part of attempts to end years of conflict.
Mr Blah appealed to the United States to intervene and emphasised the critical situation in the capital, which he said is desperately short of food and fuel.
US commander General Thomas Turner has flown into Monrovia to hold meetings with Mr Blah, peacekeepers and the leader of the main Lurd rebel group (Liberians United for Reconciliation and Democracy).
He is seeking to secure access to relief supplies in the rebel-held port area in the capital.
The United Nations said it would return to Liberia on Tuesday to resume humanitarian operations if the security situation permits.
Tens of thousands of people in Monrovia have been isolated by weeks of fighting, while a humanitarian crisis has also been reported by the International Red Cross in the port city of Buchanan, to the east.
Mr Blah appealed to the United States to deploy its troops in Monrovia
"Please save us from this nightmare, we are suffering, we are dying," he said.
Three American warships can now be seen off the coast for the first time.
Many people hope that US forces positioned off Monrovia will now help Nigerian peacekeepers in the war-ravaged country now that Mr Taylor has left.
The US has still not committed to sending the marines ashore.
The BBC's Barnaby Phillips says that in the wake of Mr Taylor's departure, a heavy responsibility will fall on the few hundred peacekeepers in the city.
Mr Blah - who was sworn in as Mr Taylor's successor on Monday - is set to rule Liberia until October, when a government of national unity, currently being negotiated at peace talks in Ghana, is due to take over.
But Lurd rebels have rejected his appointment saying they would not recognise him or his government.
"The guns will be silent for now, but we will not co-operate politically or diplomatically," said rebel leader Sekou Fofana.
"We will be standing by, ready for any aggression by Charles Taylor's forces," he told AP news agency.
Celebrations erupted in Monrovia on Monday as Mr Taylor relinquished power.
Mr Taylor's supporters wept as he boarded the Nigerian-bound plane, waving goodbye with a white handkerchief.
The former warlord, wanted for war crimes in Sierra Leone, and pressed to resign by Washington and by West African leaders, adopted a defiant tone as he left office, describing himself as a "sacrificial lamb".
"History will be kind to me. I know I have fulfilled my duties," he said.
"God willing, I will be back," Mr Taylor added.
He is now settling in to his new life in exile with his family in a hilltop mansion in Calabar in south-east Nigeria.