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Communities Secretary Eric Pickles has told Daybreak there is "always a risk that extremists will do stupid and unpleasant things."
He said the Woolwich attack has "actually been a catalyst to bring communities together":
London mayor Boris Johnson told ITV News that he was "absolutely confident" that people responsible for the death of solider Lee Rigby in Woolwich would be brought to justice.
He said: "People in London should realise that this is a very safe city and they can go about their business as normal."
"The killers of Lee Rigby are going to be brought to justice - I can be absolutely confident of that," he added.
He said he had no concerns about the time it took police to arrive to the incident and paid tribute to Ingrid Loyau-Kennett, a woman who confronted the alleged attackers as a man lay dead in front of them.
US President Barack Obama issued a statement in which he condemned the attacks in Woolwich yesterday, adding that he would discuss "important global security challenges our countries face together" with David Cameron in June.
A terror expert warned the killing of a soldier in Woolwich was "likely to be the kind of attack we will see in the future".
Dr Christina Hellmich, an expert on al-Qaeda and international terrorism at the University of Reading, said:
Peter Clarke, who led the investigation into the 7/7 London bombings, said that if the Woolwich attackers did turn out to be acting alone, it showed the difficulty the security services faced in trying to stop them.
"An attack like this doesn't need sophisticated fund raising and sophisticated communications or planning," he told Reuters. "It can be organised and then actually delivered in a moment."
The Mayor of London has tweeted a picture of him and the Prime Minister meeting community leaders in Woolwich.
Boris Johnson tweeted: "Earlier today, I met with community leaders in Woolwich alongside David Cameron and local MP Nick Raynsford.
"Clear and overwhelming message from the community meeting - London won't be divided by this sickening atrocity."
Speaking in Israel, Foreign Secretary William Hague responded to the Woolwich soldier murder. He said: "As our Prime Minister said this morning, we will never give into terror."
Israeli Prime Minister Benjamin Netanyahu added: "We wish to send our condolences to the family and to the people of Britain... We sympathise deeply."
Latest ITV News reports
In an article for ITV News, former Home Secretary Jacqui Smith reveals the pressures the Government faces after a "terrorist attack".