West African peacekeepers have started patrols in the capital, Monrovia, for the first time since arriving at Liberia's main airport on Monday.
Liberians hope the fighting is now over
The BBC's Barnaby Phillips in Monrovia says that thousands of people shouting "We want peace, no more war" spilled out onto the road from the airport and mobbed the Nigerian soldiers as their convoy went past.
Our correspondent says that the peacekeepers looked extremely pleased with their rapturous welcome and waved white handkerchiefs as a symbol of peace.
Initially they will be patrolling in the government-held south and east of Monrovia, before going to rebel-held areas later on.
Some four weeks of bitter fighting in the capital has ceased since some 400 peacekeepers started arriving at Robertsfield airport, 40km from the city centre.
'Wait and see'
Meanwhile, an emergency session of parliament has approved President Charles Taylor's plans to step down and hand power to Vice-President Moses Blah on Monday.
He had planned to make an official speech but sent a three-page letter instead, in which he pointed to an "international conspiracy" against him.
"Therefore I, the president of this noble republic, can no longer preside over the suffering and humiliation of the Liberian people," he said.
But in an earlier interview, he said that because of "security" concerns, he would not publicly announce when he will leave to take up an offer of asylum in Nigeria.
The chairman of the second largest rebel group, Model, Thomas Nimely, has told the BBC's Focus on Africa programme that Mr Taylor's forces are continuing to attack the port city of Buchanan.
Mr Taylor has said he will leave Liberia to take asylum in Nigeria, but a spokesman for the Nigerian president said that Mr Taylor was now waiting for the charges against him to be dropped before leaving.
A United Nations-backed war crimes tribunal has issued an international warrant for his arrest for his alleged role in the brutal 10-year civil war in neighbouring Sierra Leone.
Liberia has asked the International Court of Justice in The Hague to rule that the warrant for his arrest is invalid.
The leader of the main rebel group says that the charges against Mr Taylor should be dropped if that would persuade him to leave the country.
"We agree that charges against him could be dropped if it can bring peace to the country, if that can get him to leave Liberia," said Sekou Damate Conneh, from the Liberians United for Reconciliation and Democracy (Lurd) group.
People in the capital are desperate for food, especially in government-held areas, where products such as rice cost 20 times more than in the port area controlled by the rebels.
The humanitarian situation seems to be better in rebel-controlled parts of the city because they have been distributing the stocks of food which were in the port's warehouses, reports the French news agency, AFP.
However, the international medical teams in Liberia have remained on the government side of the front line.
Won 1997 elections
Accused of backing brutal Sierra Leone rebels
The World Food Programme says that a ship carrying food and equipment is due to arrive off Monrovia on Thursday and will dock when the port area is secure.
On Tuesday, the rebels promised West African peacekeepers that aid agencies could use the port in the capital, Monrovia, to deliver badly needed supplies of food, water and medicine, West African peacekeepers said.
Rebel leader Mr Conneh told the BBC's Network Africa programme that his forces would cede control of the port area to Ecomil and withdraw to the River Po, 12 km from the city centre.