The party's vice president said security officials read out an order to him banning the party from political activities.
But Foreign Minister Mustafa Osman Ismail said the party had not been banned.
"That's not true," he told reporters in Khartoum on Saturday. "It's up to them to continue their political activities," he said, adding the party had been banned only from holding the rally because it did not have the proper security permission.
Party spokeswoman Mariam al-Mahdi, also Sadiq's daughter, said the security services had released the party officials.
"But they are still daily monitoring our movements, detaining our people and they have banned our students from holding rallies," she told Reuters.
The U.N. Security Council has passed a resolution calling for Sudan to refer all alleged war criminals in the country's western Darfur region to the International Criminal Court (ICC).
The government rejected the resolution and has called for a mass mobilisation of people and political parties to oppose what it calls a violation of Sudan's sovereignty.
In contrast, Darfur rebels welcomed the resolution, saying they would send any of their members who are accused of war crimes to the ICC.
Tens of thousands have been killed in more than two years of open revolt in Darfur, with more than 2 million fleeing their homes to makeshift camps in the area the size of France.
The United States calls the violence genocide and a U.N.-appointed commission said heinous war crimes had taken place.
Chad, which hosts more than 200,000 Sudanese refugees from the conflict in neighbouring Darfur, on Friday accused Sudan of threatening its security by recruiting and arming 3,000 Chadian rebels close to the border.
Ismail said he had called high-level Chadian officials in the capital and investigations would begin into the reports.
Chad has mediated talks to solve the Darfur crisis. Chadian President Idriss Deby is the same tribe as many of the Darfur rebels, Zaghawa, whose people straddle the Chad-Sudan border.