Alliance fighters have set up checkpoints in Kabul
The movement's fighters entered Kabul unopposed to scenes of chaos and jubilation on Monday night after a series of sweeping advances in the north.
They have now occupied government buildings and set up checkpoints in the city.
Alliance Foreign Minister Abdullah Abdullah sought to allay international concern by inviting UN representatives into Kabul along with other Afghan groups for discussions on the country's future administration.
"Taliban excluded," he told a news conference in the capital.
UN Secretary-General Kofi Annan has urged the Security Council to avert a security vacuum in Afghanistan and back efforts to form a broad-based government.
The Pakistan-based Afghan Islamic Press says Mullah Mohammed Omar told his men from his southern stronghold of Kandahar to obey their commanders and not to desert.
Click here for map of the battlegrounds
Backed by US bombing, Northern Alliance troops broke through two lines of Taleban trenches north of Kabul on Monday, advancing quickly on the capital.
The Northern Alliance had said it would heed calls for it not to take Kabul until a government representing Afghanistan's many different groups could be formed.
The country's former King, Zahir Shah, has accused the Northern Alliance of reneging on earlier promises.
"This was something new and beyond our expectations," his spokesman, Abdul Sattar Sirat, said.
Many in the capital remember years of bitter factional fighting which reduced much of Kabul to rubble in the early 1990s.
Mr Abdullah said, however, that security concerns had left the former opposition with little option but to enter the city, where it had now massed a 6,000-strong force.
In other developments:
Old freedoms return
Residents of Kabul said music - banned by the Taleban - was broadcast on Kabul radio for the first time in five years.
"You can celebrate this great victory," a female announcer told residents - another novelty in a city where women have been banned from most work and education since 1996.
And men have been queuing at barbers' shops to have their beards shaved off - another gesture of freedom from the strict Taleban interpretation of Islam.
The Kabul office of Qatar-based al-Jazeera television took a direct hit from a US bomb overnight. The building was destroyed, but the staff had already left the building.
BBC correspondent William Reeve says a US bomb landed earlier on a house about 100 metres from the BBC office where he was broadcasting. The blast smashed all the office's windows.
Northern Alliance gains
The advance followed sweeping gains by the Northern Alliance across the north of the country on Monday.
The alliance has also taken control of the key western city of Herat and is pursuing retreating Taleban forces in the north-eastern Kunduz province.
Herat commands vital highways leading to Iran and Turkmenistan.
It could also be the gateway for an advance on Kandahar.
Correspondents say the war in southern Afghanistan could be very different, as the Northern Alliance itself may be unwilling to press on into largely Pashtun territory.
The Taleban leader, meanwhile, is reported to have ordered his troops to regroup and fight.
His Majesty is concerned about the safety of the people
Spokesman for ex-King Zahir Shah
BBC defence correspondent Jonathan Marcus says the hunt for Osama Bin Laden, wanted for September's devastating attacks in the US, may only move into high gear once more of the country is in the hands of groups friendly to the US.
As they neared Kabul, villagers stood cheering, some throwing flowers on alliance tanks as they drove past.
