The BBC is planning to increase its coverage of non-Christian religions and could broadcast Muslim Friday prayers after claims that its output is too Christian, according to The Times.

Lord Hall of Birkenhead, the BBC's director-general, is reportedly inviting religious leaders to join discussions about plans for more multi-faith coverage and will appoint a senior executive, who will sit on the board of governors, to draw up new programme ideas alongside broadcasts such as Songs of Praise and Thought for the Day.

The Times reported that sources had made clear that increased multi-faith coverage will not be at the expense of Christian output. However, the reported revamp comes after criticism that Muslims, Hindus and Sikhs were being ignored, and an internal BBC report which concluded that there was a disproportionate amount of programming on Christianity compared with other faiths.

Earlier this year Aaqil Ahmed, the head of religion and ethics at the BBC who recently announced he would be leaving the corporation, told a House of Commons committee that he had prepared a report for Lord Hall outlining the religious mix. "Christianity remains the cornerstone of our output and there are more hours dedicated to it than there are to other faiths," he said.

The Times said that Lord Hall was determined to do more to more represent other faiths. "Faith is remarkably important," a source was quoted as saying by the newspaper. "The BBC can and must do more to ensure that the important role faith plays is recognised and reflected in our programming."

Religious leaders likely to be invited to the discussions include Justin Welby, the Archbishop of Canterbury; Cardinal Vincent Nichols, the Archbishop of Westminster; Ephraim Mirvis, the Chief Rabbi; Harun Khan, the head of the Muslim Council of Britain, and Hindu and Sikh leaders.

Ibrahim Mogra of the Muslim Council of Britain reportedly said that the BBC could televise Friday prayers from a mosque, cover Eid, or children attending Koranic lessons.

A spokesperson for the Board of Deputies of British Jews said: "We would love to see a programme exploring the history of Jewish-Muslim co-operation over the centuries, such as during the Holocaust when many Jews were saved by Muslims."

In September, the BBC appointed the former interviewer Martin Bashir as its new religious affairs correspondent.