A row over whether Sudan's capital, Khartoum, should be subject to Islamic law has hit relations between former rebels and its partner in government.
Khartoum is in the mainly Muslim north, but also hosts many non-Muslims
This question was a key part of a last year's deal to end 21 years of war between the mainly Muslim north and the Christian and animist south.
But the BBC's Jonah Fisher in Khartoum says the deal was vague on the details.
Violence has risen, due to frustration over the lack of rebuilding in the south, a UN envoy said this week.
Pol Ring, head of the former rebel SPLM in Khartoum's parliament, said the draft constitution propsed for the city was the same as the existing Sharia law.
This was unacceptable because Khartoum is the capital for the whole country, he said.
The SPLM has now pulled out of the committee drafting Khartoum's new constitution.
Southerners who live in the capital's slums are routinely arrested and beaten for brewing home-made alcohol.
Our correspondent says under the peace deal, Sharia law will continue, with special protection for non-Muslims.
UN Sudan envoy Jan Pronk's warning came as the repatriation of refugees to the south was suspended for two weeks after heavy fighting at the weekend.
Despite $4.5bn in aid being promised to the south, only a tiny fraction of that has actually been delivered.
With the volatile mixture of ethnic groups, age-old grievances and weapons, bringing stability to southern Sudan was always going to take more than a peace agreement between the northern government and the southern rebels, our reporter says.