The semi-autonomous Muslim island of Zanzibar already has the Kadhi courts
Churches in Tanzania have petitioned against a proposal to set up Kadhi (Islamic) courts to handle disputes among the Muslim community.
They will create religious tension in a country that prides itself on high levels of religious and social tolerance, the church leaders say.
The petition was signed by 64 leaders from the Christian Council of Tanzania (CCT) and Pentecostal churches.
A BBC reporter says public opinion is sharply divided over the issue.
MPs were also split over introducing Kadhi courts, which deal with domestic issues such marriage and divorce, during parliament's session in August.
Muslims make up nearly half of the population on mainland Tanzania.
The semi-autonomous archipelago of Zanzibar, where 99% of the population is Muslim, has had Kadhi courts as an official part of its justice system since 1985.
The BBC's John Ngahyoma in the main city of Dar es Salaam says that although the government has not yet made a decision, there is a good chance that it will allow the courts.
The government is also considering joining the Organisation of Islamic Conference (OIC), a move that has been met with criticism by Christian leaders.
Foreign Affairs and International Cooperation Minister Bernard Membe said the government would seek the people's consent on whether Tanzania should join the OIC, Tanzania's Guardian newspaper reported on Thursday.
Church leaders say that joining the OIC would contravene the country's constitution as Tanzania is a secular state.