Deputy PM Nick Clegg quoted from the Koran as he told a meeting of faith leaders Islam had been "perverted" by the alleged murderers of Lee Rigby.
Speaking alongside politicians from other parties, the Lib Dem leader called for people of all faiths to present a united front against terror.
He said a message of "hope over fear, of community over division" was "immensely important".
He called on people to resist a "fear" in the aftermath of the murder.
Mr Clegg was approached by leaders in the Muslim community asking for him to work with them to bring together people from all faiths and backgrounds to demonstrate that London stands united against all forms of extremism.
Clegg cited verse 32 chapter 5 the Koran, which says: "If anyone kills a human being it shall be as though he killed all mankind whereas if anyone saves a life it shall be as though he saved the whole of mankind."
'Feeling of fear'
He added: "A religion of peace was being distorted, turned upside down and inside out, perverted in the cause of an abhorrent and violent set of intentions.
"Terrorism has no religion because there is no religious conviction that can justify the kind of arbitrary, savage random violence that we saw on the streets of Woolwich."
He called on people not to allow the attack to frighten them into disrupting their normal way of life.
He said: "We have a choice to either allow that powerful corrosive feeling of fear to seep into every second and minute and hour of our lives or we can make a choice that we're not going to change our behaviour."
Shadow communities minister Sadiq Khan, for Labour, praised the leadership shown by the David Cameron, Nick Clegg, Boris Johnson and Ed Miliband.
Drummer Lee Rigby, 25, was hacked to death in a street in Woolwich, South London, on Wednesday afternoon.
The murder suspects Michael Adebolajo and Michael Adebowale were shot by police at the scene and remain under arrest in hospital.
Mr Khan said the phrase "Allahu Akbar" (God is great) reportedly shouted by the suspects at the scene, should not be re-appropriated from extremists.
He said: "For those who are Muslims, don't allow these people to hijack our religion or the words Allah is the greatest."
Conservative peer Lord Ahmad said: "No matter what faith you are, no matter what your background, no matter who you are what you do, together we stand united in the condemnation of a most despicable and horrific act."
Other speakers at the event included Imam Shams Ad Duha of Ebrahim College, Canon Guy Wilkinson and Leonie Lewis, co chairs of the London Faiths Forum.
On Thursday, Prime Minister David Cameron described the Woolwich attack as "deeply shocking".
"The people that did this were trying to divide us. They should know something like this will only bring us together and make us stronger," he added.