Sustained firing has broken out in the Sudanese capital of Khartoum amid tensions between the military and the country's powerful paramilitary forces.

Sudan's paramilitary Rapid Support Forces said they had taken control of the presidential palace, the residence of the army chief and Khartoum international airport.

Clashes erupted with the army in an escalating power struggle amid talks on its integration into the military under a transition plan that would lead to new elections.

US Secretary of State Antony Blinken said y the situation in Sudan was "fragile" but insisted there was still an opportunity to complete the transition to a civilian-led government.

Firing could be heard in a number of areas, including central Khartoum and the Bahri neighbourhood, on Saturday morning.

In a series of statements, the Rapid Support Forces (RSF) militia accused the army of attacking its forces at one of its bases in south Khartoum and claimed to have seized the city's airport and be in control of Khartoum's Republican Palace, the seat of the country's presidency.

The Associated Press was unable to verify those claims.

The Sudanese Army said the fighting broke out after RSF troops tried to attack its forces in the southern part of the capital.

In a later statement, the military declared the RSF a "rebel force", describing the paramilitary's statements as "lies".

The clashes came as tensions between the military and the RSF have escalated in recent months, forcing a delay in the signing of an internationally backed deal with political parties to revive the country's democratic transition.

Commercial planes trying to land in Khartoum began turning around to head back to their originating airport.

Flights from Saudi Arabia turned back after nearly landing at Khartoum International Airport, flight tracking data showed.

Footage posted to Twitter purported to show RSF troops at the airport.

Current tensions between the army and the paramilitary stem from a disagreement over how the RSF should be integrated into the military and which authority should oversee the process.

The merger is a key condition of Sudan's unsigned transition agreement.

However, the army-RSF rivalry dates back to the rule of autocratic president Omar al-Bashir, who was ousted in 2019.

Under the former president, the paramilitary force, led by powerful General Mohammed Hamdan Dagalo, grew out of former militias, known as the Janjaweed, which carried out a brutal crackdown in Sudan's Darfur region during the decades of conflict there.

In a rare televised speech on Thursday, a top army general warned of potential clashes with the RSF, accusing it of deploying forces in Khartoum and other areas of Sudan without the army's consent.

The RSF defended the presence of its forces in an earlier statement.

The paramilitary recently deployed troops near the northern Sudanese town of Merowe.

Also, videos circulating on social media on Thursday showed what appeared to be RSF-armed vehicles being transported into Khartoum, further to the south.

The US ambassador to Sudan, John Godfrey, said he was "sheltering in place with the embassy team, as Sudanese throughout Khartoum and elsewhere are doing".

"Escalation of tensions within the military component to direct fighting is extremely dangerous," he wrote.

"I urgently call on senior military leaders to stop the fighting."

In Saturday's statement, the RSF said it was contacted by three former rebel leaders who hold government positions in an apparent bid to de-escalate the conflict.