Liz Santry, Haringey Council cabinet member for Children and Young People, was responding to widespread criticism of the agencies involved.
Haringey's own report into the case of the 17-month-old boy, who suffered months of abuse despite being on the at-risk register, showed a host of failings on the part of the council, the Metropolitan Police, and health professionals.
Cllr Santry said: “On behalf of Haringey Council I would like to say how deeply saddened I am about the death of Baby P. This is a really tragic occurrence and the circumstances of his death are really dreadful.
“He died over 15 months ago, and for those past 15 months in Haringey there has been a huge amount of anguish, and endless discussion about what more we might have done to save this little boy.
“I have to say that we are truly sorry that we did not do more to protect him. Our duty is to protect our children. We did not do so in this instance and I would like to say how truly sorry we are."
In response, local MP Lynne Featherstone said it was "a shame that it has been very late in coming".
Ms Feathertone added: "They need to show this is genuine regret and not just a response to the public outcry. To do this the Leader of the Council and Lead Councillor for Children Services should now resign so we can start re-building confidence in our local child protection services.”
One of the nation's top children's services directors, John Coughlan, is to be parachuted into Haringey on the orders of children's secretary Ed Balls.
In a written ministerial statement, Mr Balls said Mr Coughlan would begin working alongside the borough's existing children's services director Sharon Shoesmith while an emergency review was carried out into the Baby P tragedy.
Mr Balls told BBC Radio 4 he was angry that a child had died in this way.
"If there are failings, there has to be accountability," he said.
An inquiry into the social workers is also being conducted by General Social Care Council (GSCC).