Earlier, state media quoted the governor of North Darfur as saying that negotiations for the trio were under way. The kidnappers are said to be demanding a ransom.
Siddig said the Sudanese government would avoid any action that could hurt the hostages.
"The kidnappers are on the move because they fear they might be attacked by security forces, but we are not going to do anything to endanger their safety," he said.
Local workers freed
The identities of the kidnappers is not known. Two Sudanese members of staff seized along with the foreigners were released shortly afterwards.
MSF pulled nearly all of its personnel out of Darfur and into the capital, Khartoum, following the kidnap. Only staff working on securing the release of their colleagues have remained behind.
The attack on the Belgian MSF branch came days after the French and Dutch contingents of the aid organisation were told to leave Darfur. The Belgian foreign ministry said that none of its nationals was involved.
MSF branches are among 13 aid groups ordered to leave Sudan after the International Criminal Court (ICC) issued an arrest warrant for Omar al-Bashir, Sudan's president, for alleged war crimes in Darfur.
Khartoum accuses the aid groups of co-operating with the ICC, which says that al-Bashir led a violent campaign in Darfur over the past six years.
The United Nations says that more than 180 foreign aid workers have left Sudan since the order by Khartoum to expel the aid groups.
The World Food Programme (WFP) says four of its partner relief agencies expelled from Darfur were looking after 35 per cent of food distribution to the region.
About 300,000 people have died in Darfur from the combined results of war, famine and disease over the course of the last six years, the UN has said. At least 2.7 million people have been displaced, it says.
The conflict in Darfur erupted after ethnic fighters rebelled against the Arab-dominated government.