The government has not previously directed the attorney-general to intervene in such religious disputes.
Anthony Rayappan, 71, who died on November 29, made news after hospital authorities refused to release his body to his family following a claim by Islamic authorities.
Both the family and Islamic authorities filed separate petitions in the civil and syariah courts seeking an order to bury the body according to their respective religious rites.
The council argued that Anthony died a Muslim after having converted to Islam in 1990.
Anthony's family, however, said he divorced his Muslim wife, renounced Islam and returned to Roman Catholicism in 1999 and remained a Christian until his death.
They said his national identity card also stated his religion as Christian.
In announcing the withdrawal, Mohamed Adzib Mohamad Isa, the council’s chairman, said they would not pursue it any further.
"I hope the matter is solved and we don't think the people will view us negatively because we made the decision based on the existing facts and not emotion."
A Catholic funeral mass is expected to be held on Friday followed by a burial on Saturday.
A similar case sparked off a national debate on religious freedom a year ago when Islamic authorities gave M Moorthy a Muslim burial despite his family’s protestations.
His widow was left without any legal recource when the High Court said it had no jurisdiction to hear her appeal.
Non-Muslims in Malaysia have been voicing concerns that the administration of Islamic law is infringing upon their right to practise their own faith.
Leaders of Muslim groups including those in the ruling United Malays National Organisation party have warned that giving minorities concessions would erode the status of Islam.
Malaysia's official religion is Islam and about 65 per cent of Malaysians are Muslims with the rest comprising Buddhists, Hindus or Christians from the ethnic Chinese and Indian communities.