About 65 people are thought to have been killed so far.
It is the first time that the conflict has reached Khartoum in decades of conflict between the country's Arab-dominated rulers and fighters from far-flung regions.
Al-Turabi denies that he has any links to JEM.
Brief detention
Earlier on Monday, Awad Babiker, al-Turabi's private secretary, said he was arrested shortly after the curfew was lifted on Sunday.
Sudan's state television had announced the lifting of the curfew in districts no longer affected by the fighting.
Babiker said that four other members of al-Turabi's Popular Congress Party had been detained.
The government accuses it of having links to JEM.
Mahjoub Fadl, press secretary of Omar al-Bashir, Sudan's president, claimed on Monday that authorities found documents confirming links between leaders of the Popular Congress Party and the JEM attack in Omdurman.
Amr el-Kakhy, Al Jazeera's correspondent in Khartoum, said: "It's well known that al-Turabi was a key partner of President Bashir in the coup that brought them to power in the 1980s.
"Since then, they have had their differences and al-Turabi was jailed. He was released on the condition that he would stay away from political life.
"Whenever something happens, al-Turabi is usually blamed - he is known for his criticism of the government."
Chad shuts border
In a related development, Chad's government announced on Monday that it was closing its eastern border with Sudan.
The move came a day after Sudan broke off diplomatic relations with Chad, accusing its neighbour of involvement in the previous day's attack.
"We are now cutting our diplomatic relations with this regime," al-Bashir had said on state television.
"These forces [behind the attack] are all basically Chadian forces supported and prepared by Chad and they moved from Chad under the leadership of Khalil Ibrahim."
The Chadian government has denied "all involvement".
Clashes persist
On the ground, Sudanese forces continue to hunt for Darfur fighters in Khartoum, where a shooting incident on Monday sent workers fleeing in panic.
Exchanges of fire also could be heard on the outskirts of Omdurman.
An interior ministry official said some fighters were still holed up in parts of Omdurman and a curfew there was extended indefinitely.
Government forces rounded up what they said were Darfuri suspects in civilian clothes.
Darfur groups said thousands of labourers from their region in western Sudan had been arrested and beaten.
And Khalil Ibrahim, JEM's leader, said on Monday that his organisation was prepared to launch further attacks on Khartoum in an attempt to topple the Sudanese government.
"This is just the start of a process and the end is the termination of this regime ... Don't expect just one more attack," he told the Reuters news agency by satellite phone.

Former allies


Both al-Turabi and Ibrahim were once part of al-Bashir's government as ideological allies.

Ibrahim, however, denounced the government in 1999 for its alleged Arab bias against ethnic Africans and took up arms.

In a recent interview, Ibrahim maintained that he and al-Turabi still had their differences.

For his part, al-Turabi fell out with al-Bashir in 1999 and has since been in and out of prison on various charges, and under house arrest.