The French news agency AFP quotes an army spokesman as saying a Briton, a Norwegian, and a South African were arrested and flown to Khartoum for questioning.
Earlier this week, forces from the new nation of South Sudan withdrew from Heglig, which is claimed by both Sudan and South Sudan. Sudan is accused of carrying out an increasing number of bombings in South Sudan, which leaders in Juba say amounts to a declaration of war.
Sudan and South Sudan previously fought a 21-year civil war that killed more than 2 million people. The war ended with a 2005 peace agreement that included an independence referendum for the south.
Earlier this week, the United States presented a draft resolution to the U.N. Security Council warning Sudan and South Sudan of sanctions if they do not implement an African Union peace plan to end fighting along their border.
The AU wants the Security Council to back its peace plan, passed earlier this week. It calls for the two Sudans to settle their disputes over oil, citizenship and boundary issues within 90 days.
The Security Council has called for an immediate end to fighting along the border which, in recent weeks, has threatened to erupt into an all-out war.
Some information for this report was provided by AP, AFP and Reuters.