It called for offences of religious discrimination and incitement to religious hatred to be created.
Sir Michael Day, the commission's chairman, said the blasphemy law, which only prevents criticism of the established Church, should be extended to cover all religions or be abolished.
Last month, after the Salman Rushdie affair, the Muslim 'parliament' launched an attack on the commission and the Race Relations Act for failing to distinguish minorities on the grounds of religion.
Sir Michael responded yesterday by saying that the commission has no legal role in religious affairs, but added that he felt able to propose new religious laws because faith and race were sometimes linked.
He rejected that it was impossible to have all faiths included under a single blasphemy law because different religions competed against each other. 'Lord Scarman has said that a blasphemy law covering all religions might be possible,' he said.
Matt Cherry, spokesman for the British Humanist Association, described the idea as ridiculous. 'If you say Jesus was the son of God you are blaspheming to a Muslim and if you say he wasn't you are blaspheming to a Christian,' he said. 'Blasphemy should be abolished and no religions given special protection.'
The commission's report said that the law was discriminatory because it only protected the Church of England. But interested parties had been divided on whether this unfairness should be tackled by abolishing blasphemy as an offence or extending the scope of the law.
The Satanic Verses controversy showed that protection of religious feeling could be in conflict with 'the notion of freedom of speech', it said.
It concluded that laws against incitement to religious hatred or against discrimination on racial grounds 'would not pose the same problems in respect of freedom of speech' as a new blasphemy law.Reuse content