CSW says Revd Yat Michael from South Sudan was detained after giving a sermon at Khartoum Bhari Evangelical Church. Local authorities said they were offended by his reference to the demolishing of a church building in his sermon.
Revd Peter Yein Reith, also from South Sudan, was arrested shortly arriving in Khartoum. It's claimed no one has heard anything about their whereabouts since.
Restrictions against Christians have been tightened in recent months as Sudan prepares for its national elections in April.
It's also claimed opposition groups have been targeted by authorities in the run up to the vote.
Speaking about the situation in Sudan, CSW's Chief Executive Mervyn Thomas said: "CSW is deeply concerned by the continuing arbitrary and incommunicado detention of Revd Michael and Revd Reith, in violation of Sudan's obligations under the International Covenant on Civil and Political Rights (ICCPR), which the country has signed and ratified and which in Article 9:1 prohibits arbitrary detention.
"Furthermore, the continuous interference by the Sudanese authorities into the affairs of religious institutions is in violation of Article 18 of the ICCPR.
"We urge the Sudanese authorities to release Rev Michael and Rev Reith unconditionally and without delay, to cease the campaign of harassment against Mr Obid and his family and restore their property.
"We also urge the government to release detained opposition leaders, end its restrictions on civil society and facilitate the drafting of a constitution reflecting the nation's religious, cultural and ethnic diversity."