The opposition's advance has been spectacular
In a statement to Parliament, he said anti-Taleban forces were now beginning to succeed in the south of the country, following their sweeping advance south into Kabul on Tuesday.
Mr Blair said: "It is now clear that the Taleban regime is in a state of collapse across Afghanistan".
He was speaking as reports emerged that the Taleban had been forced out of several eastern provinces, and might be losing their grip on the southern stronghold of Kandahar.
Defiant
Despite these territorial losses, the Taleban leadership remained defiant, claiming to be regrouping after what they called a tactical withdrawal from some cities.
But Mr Blair rejected this, saying the claim was a "lie".
US Defense Secretary Donald Rumsfeld said it was gratifying to see the Afghan people getting their country back, but admitted that key Taleban leaders were still at large.
Speaking during a tour of the World Trade Center ruins in New York, Mr Rumsfeld said US special forces were watching key roads in southern Afghanistan as the Taleban fled southward.
He said that capturing the Taleban leaders and al-Qaeda's leader Osama Bin Laden, chief suspect in the 11 September terrorist attacks, would not be easy.
"Finding a handful of people is indeed like finding a needle in a haystack," he said.
In other developments:
Retreat
Taleban forces appeared to have retreated towards the northern town of Kunduz, where they are surrounded, and to Kandahar in the south.
The BBC's Adam Brookes reports from the Chaman border crossing that Taleban fighters making their way into Pakistan said their comrades in Kandahar were still entrenched and ready to fight.
But refugees crossing the border said there were noticeably fewer Taleban in the city, while aid workers said morale among the remaining fighters was low and several commanders had gone to seek refuge in the surrounding mountains.
Pentagon spokesman Rear Admiral John Stufflebeem said there had been fighting around Kandahar's airport, but it was not clear which tribes were fighting the Taleban, or who was now in control of the site.
The Northern Alliance says there have been popular uprisings in the four eastern provinces of Laghman, Logar, Kunar and Nangahar and that the Taleban have abandoned the central province of Uruzgan.
Click here for map of the battlegrounds
Jalalabad
The BBC's correspondent in Peshawar, Daniel Lak, says Taleban troops have also largely abandoned the eastern city of Jalalabad.
But with rival tribal leaders apparently competing for power, there are conflicting reports about who controls it now.
The head of a newly established Southern Council of Afghanistan, Haji Gardezi, said at least five provinces in the Taleban heartland in central and southern Afghanistan were setting up their own administrations.
The Northern Alliance Interior Minister, Yunis Qanuni, said the Taleban now controlled less than 20% of Afghanistan, as more provinces declared themselves free of their control.
The Northern Alliance have taken control of the key western city of Herat and are preparing to attack Kunduz - the last Taleban foothold in northern Afghanistan.
Taleban 'regrouping'
But Taleban deputy ambassador Sohail Shaheen told Reuters TV that the militia was regrouping.
"In all these provinces there is no clash," Mr Shaheen said. "It was a strategic and tactical withdrawal from all these provinces."
Referring to the Northern Alliance's takeover of Kabul, he said: "We wanted to save the lives of the civilians of Kabul. For the protection of their lives we withdrew from Kabul."
In the capital, Alliance troops have killed at least 11 Arabs and Pakistanis they suspected of supporting the Taleban or al-Qaeda.
