The reward for the Jem leader's capture has doubled to $250,000
Sudan has asked the international community to list the Darfur rebel that led the weekend attack near the capital as a terrorist group.
It wants Justice and Equality Movement leaders living abroad to be handed over to the authorities in Khartoum.
Meanwhile, the officer heading Darfur's peace force says Saturday's raid in which more than 220 people died will set the Darfur peace process back.
He told the BBC it would harden attitudes and bring more suffering.
Gen Martin Luther Agwai commands the 9,000-strong UN-African Union force which is responsible for trying to protect civilians and maintain peace in Darfur.
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.
The BBC's Amber Henshaw in Khartoum says mass arrests continue to be carried out across the city as the authorities search for rebels still hiding or anyone linked to them.
Human rights activists say they are concerned about people being mistreated, tortured or even killed.
They say hundreds of Darfuris are being rounded up; the government says anyone arrested in connection with the attack will be given a fair military trial.
Sudan has accused neighbouring Chad of backing Jem, which Chad denies, and doubled the reward for the capture of Jem leader Khalil Ibrahim to $250,000.
At a televised rally on Wednesday morning, Sudan's President Omar al-Bashir said the rebels were backed by Israel.
In response the tens of thousands of people in the crowd chanted: "You are an agent, Khalil, you are an agent of Israel", Sudan TV reports.
Senior Sudanese foreign ministry official Mutrif Siddiq said it was unacceptable for the rebels to have attempted to topple a legitimate government.
He said the government has more evidence to prove Jem is a terrorist organisation and a dossier on Saturday's lightning-speed attack as well as alleged crimes committed in the past was being prepared.
"We think that it is beyond doubt that Jem is a terrorist organisation and through diplomatic means we are going to ask them to hand over all the Jem leaders in other countries," Reuters news agency quotes Mr Siddiq as saying.
Our correspondent says Jem is known to have or have had representatives in London, Cardiff, Egypt and Libya.
Jem was founded by Darfuris loyal to Islamist leader Hassan al-Turabi, whose party instigated President Omar al-Bashir's 1989 coup.
When Mr Turabi fell out with Mr Bashir over reducing the president's powers 10 years later, his supporters were purged from government.
It was some of those from Darfur removed at this time who went on to found Jem led by Mr Ibrahim, who wrote The Black Book: Imbalance of Power and Wealth in the Sudan.
Our correspondent says it is difficult to know their exact size.
The defence minister said the attack on Omdurman involved 300 rebel vehicles; some say this could mean up to 3,000 fighters.
An army spokesman said on Tuesday that at least 91 rebels were killed in the clashes and a large number of injured fighters were in hospital.
He said many more had died in fighting in neighbouring Kordofan province at the end of last week but could not give an overall figure.
These developments spell disaster for the peace process as far as the peacekeepers are concerned.
"The peace process will be put to the back burner," Gen Agwai told the BBC's Network Africa.
"It will lead to more suffering, more displacement, more hunger in the whole Darfur region."
Chad has closed its border, saying Sudan is planning an attack.
He said that peacekeepers will now have to spend more time watching the border with Chad than protecting civilians.