The move, by the Christian Association of Nigeria (CAN) comes six weeks after the northern state of Zamfara implemented sharia - the Islamic system of justice, drawn directly from the Koran. As the Ramadan fast began on Thursday, other Muslim-dominated states in the huge West African country were signalling their intent to follow suit.
Nigeria, which with more than 100 million people is Africa's most populous country, combines traditional religions with Christianity and Islam. There is no reliable estimate of which religion dominates nationally but Muslims are in a large majority in the north, the east is mainly Christian and the south-west is mixed.
CAN, which represents Protestant and Roman Catholic churches, claims that the implementation of sharia is unconstitutional because Nigeria, under its new civilian constitution, is a secular state.
The organisation's general secretary, Charles Obasola Williams, said: "There seems to be a sinister motive to this sharia decision. We have written to the attorney general calling on him to take action against Zamfara. If he does not, we will consider taking our own legal action.
"You cannot have two systems of law - common law and sharia. Many states in the north are now talking about sharia but this runs counter to the well-integrated nature of many parts of the country where there is intermarriage and peaceful cohabitation. We know sharia will work against Christians," he said.
But the current trend, as Nigeria grapples with ethnic tensions, is towards the spread of the official use of sharia in Muslim areas. On Monday, members of the state assembly in Kano, the most populous region of the north, tabled a Bill calling for sharia. They said that non-Muslims in Kano would be excluded from sharia, as in Zamfara. But CAN and other critics argue that this is an impossibility because the enforcement of rules such as the ban on drinking alcohol would necessarily affect Christians.
Sharia has reportedly been very popular in Zamfara and the state's Muslim leaders are now claiming it is the most law-abiding area of the country. As yet, Zamfara's community courts are not known to have recommended any controversial punishments, such as the amputation of hands for thieves.
Rivers State, in the southern delta region, has threatened to respond by declaring itself a Christian state. CAN also wants Nigeria to withdraw from the 52-nation Organisation of Islamic Conference (IOC), which it joined under military rule.
President Olusegun Obasanjo, who took office after democratic elections in May, is grappling with a number of ethnic challenges.
Two weeks ago, he sent troops into the village of Odi in the oil-producing Niger delta where youths from the Ijaw people were suspected of having killed 12 police officers. The troops burnt and smashed up many houses in the village, and are suspected of having killed dozens of people.
In the commercial capital, Lagos, at least 100 people died in clashes between southwestern Yorubas and northern Hausas. Up to 1,200 people are estimated by some to have died in ethnic unrest since President Obasanjo took office.
Many observers see sharia trend as a political tool to assert northern authority amid fears that President Obasanjo, a Yoruba and a Baptist, is favouring the south-west. The former military leaders, who ruled for most of the years after independence from Britain in 1960, came mainly from the north.
The Lagos-based human rights lawyer, Olisa Agbakoba, said: "Sharia has always been in effect in the north of the country. It has co-existed with common law without incident. What is different now is that, for the first time, it is being used as a political tool."