The Sudan Council of Churches has criticised the authorities for banning the construction of new churches.
Over the weekend, a Sudanese government minister said there were already enough churches to provide for Christians.
The council's secretary-general told the BBC the announcement came after a church was demolished near the capital, Khartoum, this month by town planners.
Sudan is majority Muslim, but officially guarantees freedom of religion.
Following the secession of South Sudan in July 2011, many of Sudan's Christian inhabitants moved to the South.
Shalil Abdullah, a minister of Guidance and Endowments, was quoted as saying on Saturday that the remaining churches were enough for those Christians who stayed in Sudan.
But Rev Kori El Ramli, the secretary-general of the Sudan Council of Churches, said he was surprised by the move as church leaders had always had a good relationship with the authorities.
"We are growing, we need more churches," he told the BBC's Focus on Africa radio programme.
Mr El Ramli said town planners were in the process of forcibly moving Christians from a shanty area of Omdurman city - and the church that was bulldozed had been in that suburb.
The new ruling would mean that area where the people were being relocated to - north of the city - would have no church, he said.
"We want the government to give us new plots so we can build a new church," the cleric said.
"We are citizens and the constitution says there is freedom of religion and worship so we are using this to get our rights."
The authorities had seemed recently to be taking a more threatening stance towards Christians, he added.
A workshop the council held at the University of Sudan on Monday was stopped by intelligence agents who accused them of evangelising, he said.
There was an international outcry in May when Sudanese woman Meriam Yahia Ibrahim Ishag, who is married to a Christian man, was sentenced under Sharia law to hang for apostasy for refusing to renounce Christianity.
Even though Mrs Ibrahim was brought up as an Orthodox Christian, the authorities considered her to be a Muslim as she was born to a Muslim father.
In June, her death sentence for renouncing Islam was overturned and she was released from jail.