Revd Yat Michael and Revd Peter Reith were reportedly stopped at Khartoum Airport on Thursday and informed that a travel ban issued against them on 23 March was still in force.
The South Sudanese clergymen had been released from prison following a court hearing on Wednesday, during which Revd Michael was convicted of participation in a criminal organisation and Rev Reith of breaching public peace. Both were released on time served.
The legal team representing the clergymen immediately launched an appeal for the travel ban to be revoked, but was informed that the appeal would be heard on 9 August.
It is unclear whether it was the Prosecutor's Office or Sudan's National Intelligence and Security Service (NISS) that issued the ban.
If it was issued by the Prosecutor's Office, activists supporting the pastors say it can be overturned by the courts.
However, if it was issued by NISS, the appeal will be subject to NISS protocols and may be longer and more complex.
CSW's Chief Executive Mervyn Thomas said, "Yesterday Reverends Yat Michael and Peter Reith were released by the court. Now they are being prevented from leaving Sudan after many months were unnecessarily taken from them during their incarceration. We hope that this delay is down to a bureaucratic oversight and is not an official effort to prolong their suffering.
"We call for urgent interventions from members of the international community who have been observing the case to ensure the travel ban is lifted and that the clergymen are allowed to resume their normal lives. We also urge Sudanese officials of good will to allow these men to leave and end the ongoing harassment of Christians."
Middle East Concern is supporting the pastors and is calling on Christians to keep praying for them.
Speaking on the News Hour, Advocacy and Development Manager Miles Windsor said:"They have felt uplifted by prayer and they've really appreciated the prayers and support of people around the world.
"Keep praying for them. Do pray that they would be able to get out soon, that the travel ban would be lifted without further delay.
"In the meantime, whilst they're still in Sudan [pray] that they will know the Lord's protection and have peace about the situation."
Listen to Miles Windsor form Middle East Concern speaking to Premier's Hannah Tooley on the News Hour: