Mr Blair said aid could now be delivered more easily
At a news conference in central London Mr Blair said that with Taleban resistance largely broken the chances of ensuring a stable future government for the war-torn country had improved dramatically.
They should realise that "that we are in a far better position than we were a few days ago to make sure of the objectives not just for the international coalition but for the people of Afghanistan".
With the fall to the Northern Alliance of the capital Kabul, and large swathes of Afghanistan's north, the Taleban's resistance was now more likely to broken, the prime minister said.
A better, more stable and more broad-based government was possible and humanitarian aid could now be delivered much more effectively, Mr Blair added.
Straw 'optimistic'
Earlier Foreign Secretary Jack Straw pronounced himself "relatively optimistic" over the prospect for peace in Afghanistan - provided events move swiftly.
The foreign secretary compared the current situation in the war-torn country with Germany after it was defeated in 1945.
He said rebuilding Afghanistan was "bound to take some time".
"That happened in Germany after the war - it is almost bound to happen here now.
"The important thing is that we get on with the job right away, not suggest that there is no alternative to the chaos which has befallen that poor state for the last 20 years.
"I am relatively optimistic, because of the behaviour of the troops so far and because of the clearly expressed will of the international community to be united in a common endeavour here."
Mr Straw said speed was now of the essence in getting an interim administration that was acceptable to different tribal factions.
Speed urged
Earlier International Development Secretary Claire Short also stressed the need for speed in terms of the humanitarian mission.
She said British troops should deploy in Afghanistan "within days" to ensure aid can be got through to hungry Afghans.
A six-strong team of humanitarian experts will be sent to Mazar-e-Sharif at the weekend, Ms Short announced at a Downing Street press conference.
But to ensure effective delivery of aid a mass deployment of troops was needed, she said.
Thousands of UK troops are heading for 48-hour standby, and could be ready to go in in four days.
Mr Blair has said they could be used in future frontline offensives against the Taleban, although protection of humanitarian supplies and 'stabilising' work would be the priority.
Warning from Labour MP
But former Labour defence minister Peter Kilfoyle has warned the troops faced serious danger if they were deployed into Afghanistan.
Mr Kilfoyle cast doubt on Mr Blair's belief that the Taleban's flight from large parts of Afghanistan does not represent a tactical retreat.
Mr Kilfoyle told BBC Radio 4's Today programme on Thursday: "There seems a tremendous amount of confusion about what exactly is the situation on the ground."
British troops could become "fall-guys in inter-ethnic rivalries", he warned.
Although Taleban leader Mullah Omar remains defiant, Downing Street said on Wednesday that the "noose is tightening" around Bin Laden, who it believes is still in Afghanistan.
Mr Blair told his cabinet on Thursday - following a meeting of the war cabinet - that people should not be under the illusion that the campaign was over, despite the "collapse" of the Taleban.