Ken Livingstone may face a formal investigation into his links to controversial Muslim cleric.
Yusuf Al-Qaradawi preached in London
London's mayor caused controversy in July welcoming Yusuf al-Qaradawi who it is claimed is homophobic, anti-Semitic and condoned suicide bombers.
Now some London Assembly members say he must answer questions about how he has fulfilled his duties to foster good community relations.
The mayor said talks with Muslim leaders helps prevent terror attacks.
The call for the investigation was made after the Assembly received a dossier compiled by a coalition of Jews, Sikhs, Hindus, Muslims and gays who say they were offended by Dr Qaradawi's visit.
A decision on whether a formal investigation will be launched is expected to be taken over the next few weeks.
In a letter, rejecting the coalition's request for a meeting, Mr Livingstone said: "I cannot and do not speak for Dr Qaradawi. We would strongly disagree on a number of issues, including homosexuality."
Mr Livingstone invited the cleric to City Hall
But he added: "The fact that I do not agree with Dr Qaradawi or other religious leaders on some issues will not stop me from continuing a dialogue or sharing a platform with them on issues upon which we agree.
Over the suggestion that he is not fostering good relations between communities, he said: "The support of the Muslim communities has been essential in helping to prevent a terrorist attack in London.
"The only people who would benefit from a refusal to conduct a dialogue with eminent leaders of one of the world's great religions would be al-Qaeda and other terrorist groups who claim that a dialogue between Islam and the West is impossible.
"Qaradawi has repeatedly condemned al-Qaeda and other such terrorist groups and urged Muslims to give blood to the victims of the 11 September terrorist attacks on the United States."