The 2021 coup which the generals orchestrated derailed a transition to civilian rule.
Civilians are running out of food as the few grocery stores that remain open have been unable to replenish dwindling stocks.Â
The fighting has damaged aircraft and brought a halt to flights to and from Khartoum airport.
Blinken said a US diplomatic convoy came under fire Monday in a "reckless" action which caused no injuries.
Khartoum
Explosions shook Sudan's capital Khartoum on Tuesday evening despite one side's claiming a ceasefire on the fourth day of fighting that has killed nearly 200.
A weeks-long power struggle erupted into battles Saturday between the forces of army chief Abdel Fattah al-Burhan and his deputy, Mohamed Hamdan Daglo, who commands the paramilitary Rapid Support Forces (RSF) The two generals seized power in a 2021 coup.
Since the fighting started, international calls have mounted for an end to hostilities that have spawned increasing lawlessness, death and damage.
RSF commander Daglo, commonly known as Hemedti, announced support for an internationally-brokered 24-hour "armistice", which the army denied any knowledge of.
Gunfire in Khartoum
By 1600 GMT, the time of the supposed start to the ceasefire, gunfire could still be heard throughout the capital Khartoum, according to several witnesses, and it continued into the evening.
"As of now the fighting in Sudan, including Khartoum and various other locations, is continuing. No sign of real abatement of the fighting," the spokesman for United Nations Secretary-General Antonio Guterres said.
Daglo's announcement came after US Secretary of State Antony Blinken said he spoke with the two generals and "underscored the urgent need for a ceasefire".
Foreign ministers of the G7, which includes the US, had also called on Tuesday for the warring parties to "end hostilities immediately", as loud explosions were heard in Khartoum, where militiamen in turbans and fatigues roamed the streets.
EU envoy attacked
Underscoring the chaos, Washington said one of its diplomatic convoys was fired upon, and the EU said its ambassador was attacked at home.
Aid groups have reported looting of medical and other supplies.
There are fears of regional spill-over from the conflict that has included air strikes and artillery fire.
According to witnesses, pickup trucks carrying anti-aircraft guns — stationed in residential areas of Khartoum — were resupplied with ammunition Tuesday morning.
The windows of office and residential buildings in the city have been left shattered or riddled with bullets.
Terrified residents of the capital are spending the holiest final days of Ramadhan sheltering as tanks roll through the streets, buildings shake, and smoke from fires triggered by the fighting hangs in the air.
Others are fleeing.
"Bombardments usually start around 4am and they continue for a few hours, but today they haven't stopped," said Khartoum resident Dallia Mohamed Abdelmoniem.
"We haven't slept in the past four days," she said, adding her family had been staying indoors "trying to keep our sanity intact".
Escaping Khartoum
Families waited on Tuesday, heavy suitcases in hand, for the few buses heading south from the capital, according to AFP reporters, as more people use rare lulls in the fighting to escape Khartoum.Â
But, as many have lost power and internet connections, residents are finding it increasingly difficult to get reliable information.
Misinformation has proliferated on social media, confusing civilians anxious for accurate news about attacks and reported looting, how safe it is to move and what pharmacies are still open.
The current toll is at least 185 people killed and more than 1,800 injured, according to the UN.
Unable to reach hospitals
The true number is thought to be far higher, with many wounded unable to reach hospitals, which are themselves being shelled, according to the official doctors' union.
Four hospitals in the greater Khartoum area have been "shelled and evacuated", it said. Across the country, 16 others are "out of service", it added, while those still operating face "severe shortages" including of medical staff, water and food supplies.Â
Civilians are running out of food as the few grocery stores that remain open have been unable to replenish dwindling stocks.Â
The fighting has damaged aircraft and brought a halt to flights to and from Khartoum airport.
Damaged warplanes
Satellite photos show damaged warplanes at the airports in Merowe and El Obeid.
The Red Cross and the World Health Organisation stressed Tuesday the need for humanitarian aid corridors.
Both generals have positioned themselves as saviours of Sudan and guardians of democracy — in a country which has known only brief democratic interludes.
The 2021 coup which the generals orchestrated derailed a transition to civilian rule.
The Forces of Freedom and Change, the main civilian bloc ousted from power in that coup, rejected "the total war the generals have unleashed to destroy everything in their path".
Blinken said a US diplomatic convoy came under fire Monday in a "reckless" action which caused no injuries.
Late Monday, the European Union's top diplomat Josep Borrell reported that the EU ambassador "was assaulted" in his own home, despite the obligation of Sudanese authorities to protect diplomatic premises.
The Sudanese foreign ministry blamed the RSF for attacking diplomatic staff.
Bitter disagreements
The battles that began Saturday followed bitter disagreements between Burhan and Daglo over the planned integration of the RSF into the regular army — a key condition for a final deal aimed at resuming the democratic transition.
Both claim to be in control of key sites, including the airport and the presidential palace — none of which could be independently verified.
A number of organisations have temporarily suspended operations in the country, where one-third of the population needs aid and three UN World Food Programme staff are among the dead.
Influential northern neighbour Egypt said it had discussed with Saudi Arabia, South Sudan and Djibouti — all close allies of Sudan — "the need to make every effort to preserve stability and safety".