(Reuters) - Sudan's military launched air strikes on a paramilitary force's base near the capital in a bid to reassert control over the country on Sunday following clashes in which scores of combatants and at least 56 civilians were killed.

At the end of a day of heavy fighting, the army struck a base belonging to the government's paramilitary Rapid Support Forces (RSF) in the city of Omdurman, which adjoins the capital Khartoum, eyewitnesses said late on Saturday.

The military and RSF, which analysts say is 100,000 strong, have been competing for power as political factions negotiate forming a transitional government after a 2021 military coup.

In the early hours of Sunday morning, eyewitness heard the sound of heavy artillery firing across Khartoum, Omdurman and nearby Bahri, and there was also gunfire heard in the Red Sea city of Port Sudan, where there had been no earlier reports of fighting.

The Sudanese Doctors' Union reported at least 56 civilians had been killed and 595 people, including combatants, had been wounded since the fighting erupted on Saturday.

Scores of military personnel were also killed, it said without giving a specific number due to a lack of first hand information from many of the hospitals where those casualties were taken.

The group earlier said it recorded deaths at Khartoum's airport and Omdurman, as well as west of Khartoum in the cities of Nyala, El Obeid and El Fasher.

The RSF claimed to have seized the presidential palace, army chief's residence, state television station and airports in Khartoum, the northern city of Merowe, El Fasher and West Darfur state. The army rejected those assertions.

The Sudanese air force told people to stay indoors while it conducted what it called an aerial survey of RSF activity, and a holiday was declared in Khartoum state for Sunday, closing schools, banks and government offices.

Gunfire and explosions could be heard across the capital, where TV footage showed smoke rising from several districts and social media videos captured military jets flying low over the city, at least one appearing to fire a missile.

A Reuters journalist saw cannon and armoured vehicles on the streets and heard heavy weapons fire near the headquarters of both the army and RSF.

Army chief General Abdel Fattah Al-Burhan told Al Jazeera TV the RSF should back down: "We think if they are wise they will turn back their troops that came into Khartoum. But if it continues we will have to deploy troops into Khartoum from other areas."

The armed forces said it would not negotiate with the RSF unless the force dissolved. The army told soldiers seconded to the RSF to report to nearby army units, which could deplete RSF ranks if they obey.

The RSF leader, General Mohamed Hamdan Dagalo, better known as Hemedti, called Burhan a "criminal" and a "liar".

"We know where you are hiding and we will get to you and hand you over to justice, or you die just like any other dog," Hemedti said.

A prolonged confrontation could plunge Sudan into widespread conflict as it struggles with economic breakdown and tribal violence, derailing efforts to move towards elections.