Tony Blair held talks with Spain's Jose Maria Aznar
It is still not known for sure what advances have been made by the opposition forces, who claim they have taken the city, but Mr Blair said it was clear that they were "substantial".
With their talks agenda including the war on terror, the British prime minister told reporters the coalition was "as strong today if not stronger than it was on 11 September".
"I think at every level - political, diplomatic, military - the momentum is now against the Taleban regime and the terrorist network in Afghanistan.
"As we can see from the advances made in and around Mazar-e-Sharif in northern Afghanistan, that momentum is continuing.
"There is only one outcome and that will be ensuring that the objectives of our campaign are met and met in full."
State of play
Pressed on what information there was about the Northern Alliance claims, Mr Blair said although it was known "there has been substantial progress in the taking of Mazar-e-Sharif, we don't know exactly what the current state of play there is".
There was a growing diplomatic sense that it was possible to put together a regime not headed by the Taleban, he went on.
"Taking all these things together I think there is significant progress being made."
According to Northern Alliance spokesman Ashraf Nadeem, their forces entered Mazar-e-Sharif and took over the airport earlier on Friday.
No confirmation
He told Reuters by telephone: "Taleban forces are fleeing towards Kabul."
There is no independent confirmation of the claim, but earlier the Alliance reported that the Taleban appeared to have abandoned the city.
The Pentagon has said the situation is fluid but "encouraging".
The rapid developments came as Mr Blair prepared for a weekend away from the world stage after a hectic series of diplomatic engagements.
The day before hosting Mr Aznar at Downing Street, Mr Blair held talks with Pakistan's President Pervez Musharraf and also with King Abdullah of Jordan.
Hours earlier he had arrived back in the UK on Concorde after a meeting with US President George Bush in Washington.
Following his talks with General Musharraf, Mr Blair said: "We want this campaign brought to a conclusion as swiftly as possible, but it has to be a successful campaign, in other words with the attainment of our objectives."
He went on to say that although the UK and its allies were "aware of the sensitivities" during the Muslim festival of Ramadan, the military campaign against Afghanistan "must ultimately continue".
On his way to London, General Musharraf called for a halt to the bombing campaign in Afghanistan, although he did not repeat that call directly as he faced the media with the UK prime minister.