Police and security forces prevented anyone from entering the Omdurman headquarters of the Umma (Nation) Party and confiscated film footage from journalists.
"The state security forces and the police have surrounded the Umma Party headquarters in Omdurman and want us to cancel the celebration tonight," the party said in a statement.
A senior official of the party, led by former prime minister Sadiq al-Mahdi, attributed the police action to the party's position in favour of cooperating with a UN resolution referring Darfur war crime suspects to the International Criminal Court.
The Security Council last week voted to refer to the court 51 people suspected of war crimes in the western Sudanese region, where a rebellion broke out in early 2003.
"All of these problems have come about because ... the Umma party's position is that we should cooperate with international resolutions," the official said.
"This contradicts the government's position because they have rejected the resolution."
On Monday, tens of thousands of Sudanese brought Khartoum's streets to a standstill as they protested against the Security Council resolution, after a government call to show opposition to what it called foreign intervention in the country.
"All of these problems have come about because ... the Umma party's position is that we should cooperate with international resolutions, This contradicts the government's position because they have rejected the resolution"
Umma Party official
Rebel groups too have welcomed the resolution and said their members would go to the court in The Hague if indicted.
The occasion was the 20th anniversary of the fall of president Jaafar Nimeiri, who was removed from office after days of street protests supported by the Umma Party.
Al-Mahdi become prime minister after democratic elections in 1986 but the current president, Umar Hasan al-Bashir, overthrew his government in a coup in 1989.
An Umma Party official said the party decided to hold the rally in their headquarters after security forces told them they could not gather in a public square.
But the armed police were determined not to allow anyone into the party headquarters for a celebration.
"Leave or we will smash you on your head," one security officer told journalists who tried to enter.
"This is our country, not yours. Get out."
Ahmad Ali Hasan, a state security officer who took television tapes from journalists, said the party did not have permission to hold the rally.
He apologised, however, for the behaviour of the forces and said the authorities would return the tapes later.