British forces could face more intense action soon
In a speech to the Welsh Assembly he said Britain would not "falter", "flinch" or "fail", adding that the US-led response to the attacks was just, and the UK must "stay the course".
The prime minister said there was now a "flood of evidence" linking Osama Bin Laden to the 11 September terror attacks on the US.
There has been criticism that after three weeks of bombing in Afghanistan, with a rising toll of civilian casualties, the allies' war aims are unclear and there is no sign when the conflict might be over.
A poll in Tuesday's Guardian newspaper suggested public support for the military action had fallen in the last fortnight from 74% to 62%.
High ground
And former Labour International Development Minister Chris Mullin, joined those calling for an end to bombing, warning there was a danger the moral high ground was being "rapidly eroded" by civilian deaths in bombing raids.
The UK's longest serving Member of Parliament, Tam Dalyell, launched a fierce attack on Mr Blair directly.
He said: "It is not moral fibre that is required. It is brains and an understanding of the Middle East.
"It is pretty galling to be told we lack moral fibre when we are asking
legitimate questions about what exactly is being attacked outside Kabul. If this
goes on during Ramadan, heaven help us."
In his speech, Mr Blair said: "It is important that we never forget why we are doing this; never forget how we felt watching the planes fly into the trade towers; never forget those answerphone messages.
"Never forget how we felt imagining how mothers told children they were about to die."
He also urged people not to forget the bravery of New York's firefighters and police officers and added "never forget the gloating menace of Osama Bin Laden in his propaganda videos".
Mr Blair said: "Never forget that long list of countries who lost sons and daughters, never forget they were of all faiths and none, many Muslims."
'Moral fibre'
The prime minister went on to say that the Taleban and their terrorist allies had one hope: "That we are decadent, that we lack the moral fibre or will or courage to take them on.
"They are wrong. We won't falter. We will not stop until our mission is complete. We will not flinch from doing what is necessary to complete it.
"We will not fail and we will do it all
because we believe in our values of justice, tolerance and respect for all
regardless of race, religion or creed just as passionately as they believe in a fanatical hatred of Jews, Christians and any Muslims who don't share their perverse view of Islam."
Mr Blair then added that the current conflict was a battle to allow the people of Afghanistan to "re-take control of their country".
Conservative defence spokesman Bernard Jenkin suggested Mr Blair's speech was more an effort to reassure the public than a reflection of any central problem over military strikes.
He said bomb attacks on Afghanistan were "degrading" Taleban capability and the US and its allies were "on course" to achieve their aims of bringing Bin Laden to justice and ensuring the country could not be used again as a base for terrorism.
'Growing public concern'
Liberal Democrat leader Charles Kennedy said there was growing public concern about military action in Afghanistan.
He attributed that concern to confusion among the public over the purpose of sustained bombing in the light of the humanitarian crisis threatening Afghanistan.
He said the Lib Dems remained supportive of the basic aims of the action but warned that the "moral authority" of military intervention would be undermined if there was a failure to deal with the humanitarian crisis.