Families of the 7 July suicide bombers should be allowed to attend the national memorial service for the victims, according to London's mayor.
Mr Livingstone said it would be offensive to turn people away
Ken Livingstone said they should not be turned away from the 1 November mass at St Paul's Cathedral for the 52 victims.
The event is billed as a service for those who died and a tribute to police, firefighters and paramedics.
Church leaders would like the bombers' families to attend but only with approval from the bereaved and injured.
Speaking at his weekly press conference at City Hall, Mr Livingstone said: "They have to decide if they want to come and share the grief of Londoners and celebrate the lives of those that were killed on the day.
"It would, I think, be particularly offensive to turn people away."
Members of the Royal Family, senior politicians and leaders from different faiths are set to attend.
Jack Nicholls, Bishop of Sheffield, said: "The families should be consulted on such an issue.
"If such a suggestion were to bring more anger between communities it would not be a risk worth taking.
"In an ideal situation it would be good for all to be able to express their grief and sorrow together and begin to look forward to building a better future where Muslim and Christian and people of any faith or none could live together in harmony."
Brian Coleman, the Tory deputy chairman of the London Assembly, labelled the idea of bombers' families attending as "political correctness gone mad", adding: "You wouldn't invite a murderer's family to the victim's funeral."
Shehzad Tanweer, 22, and Germaine Lindsay, 19, and Mohammad Sidique Khan, 30, detonated their bombs on Tube trains almost simultaneously at 0850 BST on 7 July.
Hasib Hussain, 18, blew up the Number 30 bus at Tavistock Square shortly afterwards at 0947 BST.