"While we review the evolving security situation, we are forced to temporarily halt all operations in Sudan," WFP executive director Cindy McCain said in a statement.
"WFP is committed to assisting the Sudanese people facing dire food insecurity, but we cannot do our lifesaving work if the safety and security of our teams and partners is not guaranteed."
Three WFP employees were killed and two injured in clashes in Kabkabiya in North Darfur. A WFP spokesperson told Reuters the three dead were all Sudanese.
McCain also said it was difficult for WFP's staff to operate after a U.N. Humanitarian Air Service (UNHAS) aircraft was "significantly damaged" at Sudan's Khartoum airport during an exchange of fire on Saturday.
The incident has seriously impacted the organization's ability to move humanitarian workers and aid in Sudan, he said.
The Sudanese army approved a proposal from the United Nations to open a safe passage for urgent humanitarian cases for three hours every day starting from 1600 local time (1400 GMT) on Sunday, the army said in a statement.
The army confirmed however that it will reserve the right to react if "the rebellious militia commits any violations."
Earlier on Sunday, the United Nations condemned the killing of the WFP employees, saying they died while carrying out their duties.
Volker Perthes, the head of the United Nations Integrated Transition Assistance Mission (UNITAMS), which was established in 2020 to support Sudan's democratic transition, said in a statement he was also "appalled by reports of projectiles hitting U.N. and other humanitarian premises, as well as reports of looting of U.N. and other humanitarian premises in several locations in Darfur."
"I urge all parties to respect their international obligations, including to ensure the safety and security of U.N. and all humanitarian personnel and respect the integrity of premises and assets," Perthes said, adding "civilians and humanitarian aid workers are “Not A Target.”
A power struggle between the Sudanese army and the RSF has so far killed 56 civilians and wounded 595 people, including combatants.
The fighting broke out on Saturday between army units loyal to General Abdel Fattah al-Burhan, and the Rapid Support Forces (RSF), led by General Mohamed Hamdan Dagalo, known as Hemedti. It was the first such outbreak since both joined forces to oust president Omar Hassan al-Bashir in 2019.