At least 55 Christians have been held by the Sudanese government without charge for the last two weeks.
Christian Solidarity Worldwide (CSW) says the group includes church leaders and that they have been falsely accused of receiving money from foreign countries, including Israel.
There has been a clampdown on Christians working in voluntary organisations since the end of last year.
Around a hundred foreign workers have reportedly being deported in recent months and Sudanese Christians have been detained for questioning by the security services.
A media campaign attacked "Christianisation" and was accompanied by the closure of Christian-affiliated schools, colleges and training centres, CSW reports.
The climate in Sudan has been hostile towards Christians since South Sudan gained independence in 2011.
CSW's Advocacy Director Andrew Johnston said he was deeply concerned by the arbitrary arrests.
"We urge the Sudanese government to release these prisoners and end its campaign of harassment against the Christian community" he said.
"We also urge the government once again to undertake broad consultations during the drafting of the new constitution and to ensure that it recognises the rights of all Sudanese citizens, to freedom of religion or belief, as outlined in Article 18 of the International Covenant on Civil and Political Rights (ICCPR), to which Sudan is a signatory."