Both sides appealed to their supporters to keep apart and refrain from any violence, but there was a heavy police and troop presence around potential flashpoints.
Security forces fired tear gas as pro-civilian rule protesters rallied outside parliament in Omdurman, across the Nile river from the capital Khartoum, witnesses and an AFP correspondent said.
The two sides represent opposing factions of the Forces for Freedom and Change (FFC), the civilian umbrella group which spearheaded the nationwide demonstrations that led to the army's overthrow of longtime president Omar al-Bashir in 2019.
The mainstream faction backs the transition to civilian rule, while supporters of the breakaway faction are demanding that the military take over.
Demonstrators joined the march organised by the mainstream faction in several cities across Sudan including Khartoum, its twin city Omdurman, Port Sudan in the east, and Atbara to the north.
'In the right'
Jaafar Hassan, spokesman of the mainstream FFC faction, said supporters backed two key agreements -- the 2019 power-sharing deal between the civilians the military, and a 2020 peace deal with rebel groups.
The two deals stipulate power will be handed over to civilian rule by the end of a three-year transition period in 2023.
"Our main goal is to have the military hand over the chairmanship of the Sovereign Council to the civilians," Hassan told AFP. "We also want the armed groups to be integrated in the Sudanese army."
Their rivals, the pro-military faction, have been holding a sit-in outside the presidential palace since Saturday.
It has drawn support from some of the many Sudanese who have been hit hard by the tough IMF-backed economic reforms implemented by Prime Minister Abdalla Hamdok, a former UN economist.
"We are in the right," said protester Hamada Abdelrahman, standing outside the presidential palace. "This government has not offered the Sudanese people anything for two years."
The sit-in's opponents charge it has been orchestrated by leading figures in the security forces with the support of Bashir sympathisers and other "counter-revolutionaries".
The same groups were blamed for a September 21 coup attempt that was thwarted by the government.
Ahead of Thursday's demonstrations, leaders of the rival factions appealed for calm.
Ali Ammar, a leader of the mainstream FFC, said pro-government demonstrators would stay away from the presidential palace and the cabinet building, so "there would be no friction with protesters" there.
Prominent ex-rebel figures in the pro-military faction, like Darfur governor Minni Minnawi and Finance Minister Gibril Ibrahim, called for the rival demonstrations to remain peaceful.
On Thursday, troops and police sealed off roads leading to the large open space outside army headquarters, where tens of thousands of protesters camped out for weeks before and after Bashir's ouster in April 2019.
- 'Dangerous' divisions -
Hamdok has described the deep divisions over Sudan's transition as "the worst and most dangerous" since Bashir's overthrow.
The prime minister has made his top priorities addressing the chronic economic woes inherited from the Bashir regime, and making peace with the multiple rebel groups that took up arms during its three decades in power.
A sharp improvement in relations with the United States has led to the lifting of economic sanctions giving some help to the economy.
But a package of painful structural reforms, including the slashing of fuel subsidies and a managed float of the Sudanese pound, has proved widely unpopular and has cost Hamdok's government much of its support.
In October last year, the government signed a peace deal with multiple rebel groups in Sudan's far-flung regions with a view to ending the ethnic conflicts that have dogged the country since independence.
The deal was widely hailed as a step forward, but its focus on the three battleground regions of Darfur, Blue Nile and South Kordofan left minority communities in other parts of Sudan feeling sidelined.
Resentment has been particularly strong among the Beja people of the Red Sea coast, who have mounted protests across the east since mid-September, including a blockade of the key trade hub of Port Sudan.