Diplomatic efforts have intensified to end more than two weeks of war in Africa's third-largest country as warnings multiply about a "catastrophic" humanitarian crisis.
More than 430,000 people have already been forced to flee their homes, the United Nations said.
Hundreds of others have been killed and thousands wounded.
Sudan's army chief Abdel Fattah al-Burhan and his deputy turned rival, Mohamed Hamdan Daglo, who commands the paramilitary Rapid Support Forces (RSF), "have agreed in principle for a seven-day truce from May 4th to 11th," the South Sudanese foreign ministry in Juba said in a statement.
Multiple truces agreed since fighting began on April 15 have been repeatedly violated, including one announced by South Sudan early in the war.
Witnesses reported renewed air strikes and anti-aircraft fire in Khartoum on Tuesday.
The repeated violations sparked criticism earlier Tuesday at a meeting in Addis Ababa, Ethiopia, of the Extended Mechanism on the Sudan Crisis which brought together African, Arab, UN and other representatives.
The two generals have agreed to truces, the latest one on Sunday, yet "continue fighting and shelling the city", said Ismail Wais, of the northeast African bloc IGAD which includes Sudan and South Sudan.
'No Longer Safe'
"Our priority today is to have the ceasefire prolonged and respected, then to ensure humanitarian assistance," African Union Commission chairman Moussa Faki Mahamat said, opening the meeting.
The later agreement of the week-long truce came in a phone conversation South Sudan's President Salva Kiir had with the warring parties as part of IGAD's initiative for a pause in fighting, Juba's foreign ministry said.
"We'll have to see whether this is accepted by all the parties and whether it's implemented by the forces on the ground," said Farhan Haq, the UN chief's deputy spokesman.
Kenyan President William Ruto said earlier that the conflict had reached "catastrophic levels" and finding ways to provide humanitarian relief "with or without a ceasefire" was imperative.
The UN refugee agency said more than 100,000 people were estimated to have fled to Sudan's neighbours.
Despite the dire humanitarian needs, on Tuesday the UN said its 2023 aid appeal for Sudan was $1.5 billion short.
But some relief has been arriving in the country.
After the World Health Organization (WHO) shipped in six containers of medical equipment, including supplies for treating trauma injuries, Doctors Without Borders (MSF) on Tuesday said it delivered 10 tonnes of supplies to a hospital in Khartoum as teams prepared to "launch emergency response activities."
Only 16 percent of Khartoum's hospitals are now fully functional, according to the UN.
A Sudanese physician, Howida Elhassan, posted a social media video of medical staff struggling to cope with a surge of wounded civilians at a hospital in Khartoum's East Nile neighbourhood.
Blood appeared to stain the floor of the crowded facility where patients, one who seemed to grimace in pain with blood on his shirt, lay or sat on cots.
"On days when there are battles in the area, we receive between 30 to 40 injured people," in addition to regular cases, Elhassan said. "Other medical staff cannot reach us because roads are no longer safe. We are understaffed and lack equipment."
In addition to the more than 500 killed in the fighting, 250 are estimated to be missing, said a spokesman for the Mafqud (Missing) online project.
Munira Edwin turned to the project when her brother Babiker disappeared on the first day of fighting. Mafqud called her back nearly two weeks later.
"He had been found dead with two bullets" in his body, she said, struggling to hold back tears.
It was too late on Monday, as well, for the victim who several men carried into a Khartoum hospital, covered in a grey cloth after a van was riddled with bullets. The back seat was soaked in blood. Luggage rested on the roof, as if the passengers had been trying to flee.
At risk of getting caught in the crossfire, some civilians still venture out. Long queues formed Tuesday at petrol stations offering the scarce commodity, as well as at banks and ATMs.
Ahead of the South Sudanese announcement, UN head of mission Volker Perthes said discussions involving Saudi and US mediators were underway with the rival generals to firm up a truce.
Burhan's envoy, Dafaallah al-Haj, was in Cairo where he met senior Egyptian and Arab League officials.
Haj told a press conference that he hoped the Arab League, African Union, Saudi Arabia and the US could play a role in such talks toward a more lasting truce.
While diplomats try to stop the fighting, foreign governments have scrambled to evacuate their citizens, thousands of whom have been brought to safety by air or sea in operations that are now winding down.
Russia's armed forces said on Tuesday they were evacuating more than 200 people from Sudan on four military transport planes.
Saudi Arabia said it transported another 220 people to Jeddah.
Beyond Khartoum, lawlessness has engulfed the Darfur region from where more than 70 percent of the 330,000 people displaced inside Sudan by the fighting have fled, according to the International Organization for Migration.
Darfur is still scarred by a war that erupted in 2003 when then-strongman Omar al-Bashir unleashed the Janjaweed militia, mainly recruited from Arab pastoralist tribes, against ethnic minority rebels.
The Janjaweed, whose actions led to war crimes charges against Bashir and others, later evolved into the RSF.