London (CNN) - British Muslim groups voiced their horror and condemnation

London (CNN) - British Muslim groups voiced their horror and condemnation Thursday over the slaying of a soldier in a London street by attackers who said they were acting to avenge Muslim deaths overseas.

But Muslim commentators also suggested there is more that the country's leaders can do to address issues within the Muslim community, particularly among alienated young men.

Woolwich attack: Latest developments

According to 2011 census figures, Muslims make up the second-largest religious group in Britain, with 2.7 million people. That represents an increase of 1.2 million (from 3% to 5% of the population) since 2001.

The suspected attackers in the Woolwich slaying, who are hospitalized under police guard, claimed to be acting for Islam, but it's not yet clear if they were affiliated with any group.

"The only reasons we killed this man ... is because Muslims are dying daily," said one of the suspects, wielding a cleaver with bloody hands, in video aired by CNN affiliate ITN.

"This British soldier is an eye for an eye, a tooth for tooth," he said. "We swear by almighty Allah we will never stop fighting you until you leave us alone."

The Muslim Council of Britain condemned what it called "a truly barbaric act that has no basis in Islam."

Read more: London attack mirrors plot to behead Muslim soldier

It urged Muslims and non-Muslims alike "to come together in solidarity to ensure the forces of hatred do not prevail."