Fighting has raged in the north African country since mid-April, when army chief Abdel Fattah al-Burhan and his former deputy Mohamed Hamdan Daglo, who commands the paramilitary Rapid Support Forces (RSF), turned on each other.
Multiple truces have been agreed and broken since the conflict flared, and Washington slapped sanctions on both rival generals after the last attempt collapsed at the end of May.
The air strikes and artillery bombardments that have rocked greater Khartoum almost daily subsided at least temporarily, allowing trapped civilians to venture outdoors to buy desperately needed supplies.
In one Khartoum market, people were seen scrambling to stock up on fruit and other basic goods. "The truce is a chance for us to get some food supplies after we lived on rationed quantities in recent days," said one of the shoppers, Mohamad Radwan.
Hajar Youssef said she had gone out in search of an open pharmacy to buy insulin for her mother, who has diabetes. "Unfortunately, I did not find one."
Many people expressed disappointment that the promised ceasefire was so limited in scope.
"A one-day truce is much less than we aspire for," said Khartoum North resident Mahmud Bashir. "We look forward to an end to this damned war."
Bus station employee Ali Issa said many people were using the truce to flee the capital for the relative safety of the provinces.
"Today, numbers... have risen significantly, maybe even doubled," he said.
There was no immediate word on the observance of the ceasefire in the conflict's other main battleground, the flashpoint western region of Darfur.
Announcing the latest truce on Friday, US and Saudi mediators warned the warring parties they would break off their diplomatic efforts unless they honoured their commitments this time.
"Should the parties fail to observe the 24-hour ceasefire, facilitators will be compelled to consider adjourning" talks in the Saudi city of Jeddah which have been suspended since late last month, they said.
Sudan specialist Aly Verjee said he saw little reason why this truce should be any better than its predecessors.
"Unfortunately, the incentives have not changed for either party, so it's hard to see that a truce with the same underlying assumptions, especially one of such short duration, will see a substantially different result," said Verjee, a researcher at Sweden's University of Gothenburg.
Upwards of 1,800 people have been killed in the fighting, according to the Armed Conflict Location and Event Data Project.
Nearly two million people have been displaced, including 476,000 who have sought refuge in neighbouring countries, the United Nations says.
The Saudi and US mediators said they "share the frustration of the Sudanese people about the uneven implementation of previous ceasefires".
The army said it has "agreed to the proposal", adding it "declares its commitment to the ceasefire".
The paramilitary RSF said: "We affirm our full commitment to the ceasefire."
Both statements said the truce could support humanitarian efforts, while cautioning against violations by their opponents.
"If observed, the 24-hour ceasefire will provide an important opportunity... for the parties to undertake confidence-building measures which could permit resumption of the Jeddah talks," the US-Saudi statement said.
Friday's ceasefire announcement came a day after Sudanese authorities loyal to Burhan declared UN envoy Volker Perthes "persona non grata", accusing him of taking sides.
UN chief Antonio Guterres later expressed support for Perthes, who is currently in the Ethiopian capital Addis Ababa for talks.
Speaking through his spokesman, Guterres said "the doctrine of persona non grata is not applicable to or in respect of United Nations personnel."
The fighting has sidelined Perthes's efforts to revive Sudan's transition to civilian rule, which was derailed by a 2021 coup by the two generals before they fell out.
It has also complicated the coordination of international efforts to deliver emergency relief to the 25 million civilians that the United Nations estimates are in need.