Human rights groups say they are worried about the possible torture of those detained since the Darfur rebel weekend attack near Sudan's capital.
There are also unconfirmed reports of summary executions of Darfuris, say Human Rights Watch and the Aegis Trust - quoting eyewitnesses.
The government promised that anyone arrested in connection with the attack would receive a fair military trial.
At least 220 people died in the raid, including 34 civilians, the army says.
Since Saturday hundreds of people are believed to have been arrested on suspicion of backing the Darfur rebels.
"People are identified and treated openly in a harsh way because of their colour or because they look Darfuri"
Saturday's raid on Omdurman, Khartoum's twin city across the River Nile, was the closest Darfur's rebel groups had come to the capital in five years of conflict in the region.
Sudan has accused neighbouring Chad of backing the Justice and Equality Movement (Jem) rebels and cut diplomatic relations.
Chad has denied the charges and closed its border, saying Sudan is planning an attack.
Sudan's government has doubled the reward for the capture of Jem leader Khalil Ibrahim to $250,000.
International law
New York-based Human Rights Watch said it had received unconfirmed reports that two of those arrested had been executed in public.
An eyewitness told UK charity the Aegis Trust that a woman walking with her brother in Omdurman on Sunday was stopped by four members of the security forces.
"They ordered the youth to put up his hands. The woman protested that this was her brother. One of the security men pulled out his gun and shot her in the face. She fell down dead," the witness said.
Human rights lawyer Saleh Mahmoud Osman said hundreds of Darfuris had been rounded up, including his brother.
"On public transport, even on the streets, people are identified and treated openly in a harsh way because of their colour or because they look Darfuri," he told Reuters news agency.
The BBC's Amber Henshaw in Khartoum says state security agents have been conducting house-to-house searches for suspected rebels in the city.
She says some checkpoints around Khartoum have been removed but they remain on strategic bridges and in Omdurman.
On Monday, a curfew was re-imposed in Omdurman and our correspondent says the atmosphere remains tense.
Mohammed Zaroug from Sudan's embassy in London told the BBC's Focus on Africa programme that all of those arrested would be treated according to both Sudanese and international law.
The government says it has crushed the rebel attack but the Jem leader says the rebels will be back.
"This is just the start of a process and the end is the termination of this regime," Mr Ibrahim told Reuters.
Experts say Chad and Sudan are fighting a proxy war using each other's rebels to achieve their military objectives.
Chad President Idriss Deby has blamed Sudan for supporting a Chadian rebel attempt on the presidential palace in the capital N'Djamena in February.
Sudan's Islamist leader Hassan al-Turabi was accused of having links to the rebels, and was detained on Monday and interrogated for several hours by the security forces over the attack.
He was freed from custody some hours later.
Mr Turabi has in the past denied such allegations, although some Darfur rebel leaders, including Mr Ibrahim, have followed him.
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