Muslim groups have united in condemning the attack in Woolwich as un-Islamic.
The Muslim Council of Britain said the killers' use of "Islamic slogans" indicated they were motivated by their faith.
A statement from the council said: "This is a truly barbaric act that has no basis in Islam and we condemn this unreservedly. Our thoughts are with the victim and his family. We understand the victim is a serving member of the Armed Forces. Muslims have long served in this country's Armed Forces, proudly and with honour. This attack on a member of the Armed Forces is dishonourable, and no cause justifies this murder."
The group called for vigilance and solidarity between "all our communities, Muslim and non-Muslim", and for police to "calm tensions".
Paul Salahuddin Armstrong, of The Association of British Muslims, said the attackers' actions had "removed them from Islam, because there is no grounds to justify attacks of terrorism". "If you go back to the Koran, there is no grounds for this kind of behaviour, no grounds for murder."
Akbar Khan, from Building Bridges, condemned "the killing of an innocent person" and "all forms of extremism wherever they are".
Mohammed Shafiq, from the Ramadhan Foundation, said: "I wish to condemn the evil and barbaric crime carried out in Woolwich," adding the attack "was at every level evil". He said: "London and our nation will come together and will not be divided. The terrorists will never win and succeed in their evil plans."
Fiyaz Mughal, the director of charity Faith Matters, said: "The cold-blooded killing of a serving British soldier is a crime that sickens every member of every community in the UK. We must come together, isolate those who believe that extremism and violence are acceptable, and work to ensure that they meet the full force of the law. We must send a clear message to anyone that an attack on a serving soldier going about their daily activities is something that must be utterly condemned."
Julie Siddiqi, of the Islamic Society of Britain, told the BBC Radio 4 Today programme: "We can't allow the voices of Nick Griffin and the far right to become louder than ours in the coming days. They will say what we have to say and it gives us even more incentive to speak out and come together and not allow people like that to divide us as a country.
"The people who did this act yesterday do not speak in my name, do not speak for my community or the rest of the country. We have to come out with the strongest condemnation, which is what I'm seeing this morning. All of the Muslim organisations have come out with the strongest possible terms to say there is absolutely no excuse whatsoever, no justification for anything like this. This is one of the most shocking things I have seen in recent years and to have the people of Woolwich have to experience that so close to them, I just feel is absolutely horrific."