On Sunday, Sudan cut diplomatic relations with neighbouring Chad, saying the attack by the rebels from the western Darfur region had been supported by Chadian President Idriss Deby.
The rebels made a lightning advance across 600 km (400 miles) of desert and scrub to attack Khartoum on Saturday in what one of their leaders called a bid for power.
Chad has denied involvement, but analysts say it may have backed the JEM rebels to retaliate for an attack on the Chadian capital three months ago.
Rebels in Sudan have complained for decades of neglect by the central government.
A peace deal between north and south ended one civil war in 2005 and boosted Sudan's economy by increasing oil production in the south, but that agreement did not cover the conflict that erupted in Darfur five years ago.
International experts estimate some 200,000 people have been killed and that 2.5 million have been made homeless in Darfur since mostly non-Arab rebels took up arms.
Government officials said the attack on Khartoum ruled JEM out of any peace process.
A curfew remained in force on the outskirts of Omdurman. Military checkpoints were at every major junction.
Heavy tanks lined Omdurman's streets and dozens of vehicles carrying armed men raced along. Security forces were arresting mostly young men who looked to be from Darfur.
But the streets were again full of people.
Chad said it was surprised at Sudan's "hasty decision" to cut off ties and that it hoped they would be re-established.
Deby and Bashir signed a non-aggression pact in March. Each has accused the other of breaking the deal.
