There was heavy fighting in Khartoum's twin city, Omdurman
Sudan's security forces are hunting down suspected rebels following a raid by Darfur rebels near the capital.
A BBC correspondent says there was panic in central Khartoum after police officers fired shots at a small group of people in a building.
There was also at least one arrest near the US embassy.
Sudan's Islamist opposition leader Hassan al-Turabi has been arrested and accused of links to the rebels, who on Saturday came close to the capital.
Mr Turabi's wife told the BBC that the soldiers who arrested him connected him to the weekend attack on Omdurman, the capital's twin city, just over the River Nile, where a curfew has been reimposed.
Mr Turabi denies any links to the Rebel Justice and Equality Movement (Jem) rebels but its leader used to be close to him - as did Sudan's President Omar al-Bashir.
Sudan says it has proof that neighbouring Chad backed the rebels.
The weekend attack was the closest the rebels have come to Khartoum during five years of fighting.
Jem leader Khalil Ibrahim says his group will launch more attacks on Khartoum.
"This is just the start of a process and the end is the termination of this regime," he told Reuters news agency by satellite phone.
He said he was speaking from Omdurman but this could not be independently verified.
The Sudanese government says it has learned lessons from the attack and will be better prepared next time.
Sudan's ambassador to the UN, Abdalmahmood Abdalhaleem, told the BBC that captured rebels had identified Chadian officers killed during the assault.
Sudan has severed diplomatic ties with Chad, which denies any involvement.
Mr Turabi's wife, Wisal al-Madhi, told the BBC's Network Africa programme that her husband had been away from the capital over the weekend.
She said he was arrested first thing on Monday morning.
"They had three cars full of soldiers and munitions and arms, and they took him to the prison in Khartoum North directly."
At least four other members of Mr Turabi's Popular Congress have also been arrested, party officials say.
Mr Turabi was Sudan's main Islamist ideologue in the 1990s before falling out with President Bashir. He has since been imprisoned several times.
Jem leader Khalil Ibrahim used to be one of his followers and retains an Islamist outlook.
Sudan has offered a reward of $125,000 (£64,000) for Mr Ibrahim's capture and information that leads to his arrest.
The BBC's Amber Henshaw in Khartoum says there are reports that scores of Darfuris are being picked up across the city.
Chad said it regretted Sudan's "hasty decision" to break off diplomatic ties.
Jem has also denied being backed by Chad.
Senior Jem official Tahir el-Faki told the BBC that they had already exposed the government's weakness in the assault over the weekend.
He admitted that 45 rebels had been either killed or wounded in the heavy fighting.
Founded by Darfuri Muslims loyal to Islamist leader Hassan al-Turabi
Led by lawyer Khalil Ibrahim Muhammad
Believed to have up to 3,000 fighters
Now said to have fragmented into several disparate groups
But he said that as well as further attacks on Khartoum, they would also continue to target oil installations in South Kordofan province to cut off the government's main source of income.
On Saturday, Jem rebels said they had taken Omdurman and the Wadi Saidna air force base about 16km (10 miles) north of Khartoum, and entered the capital itself.
Omdurman residents said there had been more fighting on Sunday morning.
Experts say Chad and Sudan are fighting a proxy war using each other's rebels to achieve their military objectives.
Earlier this year, rebels reached Chad's capital N'Djamena, with Chad accusing Sudan of involvement.
The Jem is one of several rebel groups fighting the government and pro-government Janjaweed militia in the western Darfur region since 2003 over alleged discrimination by the authorities in favour of Arabs.
The rebels have been involved in raids on government forces in the area before.
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