As fighting surged in the city outside, Taylor told reporters at his lavish oceanside executive offices that he would hand over power after a joint session of Liberia's congress next week.
Taylor said he would step down the morning of Aug. 11 "and the new guy will have to be sworn in by midday." But he refused to say when he would leave Liberia, as he has promised to do previously, and as West African leaders and the United States have demanded.
"The most important thing is, everything that we have said about resigning and leaving will happen," said Taylor, who has been offered asylum by Nigeria.
Taylor has said he will hand power to one of two longtime colleagues - Nyundueh Monkomana, Liberia's speaker of the house, or Moses Blah, his vice president.
The president had accused Blah of complicity in what he called a U.S.-backed coup attempt against him in June, but Blah eventually returned to what appeared to be his full public role. Monkomana is thought more acceptable to all sides, including rebels.
Taylor has been promising to surrender power since June 4, when a U.N.-Sierra Leone court announced a war-crimes indictment against him for his support of rebels there in a brutal civil war.
He also has made and broken other accords in 14 years of Liberian conflict, which Taylor, then a warlord, started as the leader of a small insurgency in 1989.
Saturday's meeting appeared to make at least some progress by committing Taylor to a date.
West African heads of state, in a summit late last week in Ghana, committed to sending peacekeepers Monday to Liberia, where rebels pressing a 3-year-old war to oust Taylor have the capital under two months of deadly sieges.
They had insisted that Taylor leave by Thursday, three days after the deployment - an unusually forceful message to a peer, delivered under strong U.N. and U.S. pressure.
"West African leaders seemed to understand that leaving the country within three days is not practical," Taylor's spokesman, Vaanii Passawe said after the meeting.
One envoy praised Taylor's agreement as "unprecedented."
"He is to be congratulated for his sense of statesmanship and patriotism, recognizing the realities and the fact that his departure will facilitate the making of peace in Liberia," Nana Akufo-Addo, Ghana's foreign minister, said. "That's our main concern, not deadlines."
The U.N. Security Council on Friday approved deployment of the multinational force to Liberia, which is to last two months and be followed by U.N. peacekeepers.
It was still unclear whether U.S. Marines on three warships that are expected to arrive off Liberia's coast soon will go ashore. The Bush administration has insisted that the force being assembled by the Economic Community of West African States, known as ECOWAS, take the lead.
But Liberians - who feel a historical and cultural bond with the United States - have clamored for U.S. forces to help end the fighting in their country, founded by freed American slaves in the 19th century. Liberia remained a commercial and then strategic partner of the United States up to the end of the Cold War.
Fighting accompanying the rebel offensives has killed well over 1,000 civilians in Monrovia. Hostilities have cut off the port and the main water plant, leaving the city of more than 1.3 million residents and refugees desperately short of food and water, and plagued by cholera.
Heavy fighting erupted again Saturday at two bridges linking Monrovia's rebel-held island port with downtown, the heart of Taylor's government. Front line government officers, speaking on condition of anonymity, said they received an order to recapture the port "at any cost."
Government fighters crossed one span, the New Bridge, in waves, some crouching midway and directing heavy grenade and gunfire toward buildings on the other side - apparently aiming at rebel snipers. One fighter fired rounds from a .50-caliber machine gun mounted on the back of a pickup truck until he took fire and slumped over his gun.
Black smoke rose from near the port. It was unclear whether the cloud came from street fighting, government shelling, or other causes. A five-minute mortar barrage sent downtown residents cowering.
"Heavy, heavy mortars," resident Mohammed Dauda said by telephone, from under his bed. "We are taking cover."
Pickup trucks full of government fighters rolled toward the fighting. Residents and fighters claimed Taylor's forces had crossed over into Bushrod Island, site of the rebel-held port, but rebels said they had beaten them back.
The two sides traded blame for the escalation in fighting, which came as both sides sought to consolidate territory, bettering their positions for any negotiations, ahead of the arrival of peacekeepers.
At Monrovia's overwhelmed main hospital, government militia fighters brought in many of the first 70 wounded and seven or eight dead from the fighting. They slapped nurses and threatened medical workers to keep them from amputating a commander's shattered leg, hospital medical director Mohammed Sheriff said.
West African leaders have pledged to deploy at least 300 Nigerian forces on Monday, to be followed days after by troops of Ghana, Senegal and Mali. West Africans have called for a total of 5,000 regional peacekeepers.
Blah, the vice president said Saturday that Taylor set two conditions for leaving once he cedes power: that an adequate number of peacekeepers are on the ground, and that the war crimes indictment against him be dropped.
U.N. prosecutors are adamant that Taylor face justice, raising the prospect of a standoff blocking his departure.