"We confirm our full commitment to a complete ceasefire, and we hope the other party will abide by the ceasefire according to the announced time," the RSF added in a statement.
It was not immediately clear whether the army would announce its own commitment to the ceasefire.
"Life in Khartoum is impossible if this war does not stop," said Alawya al-Tayeb, 33, on her way out of the capital.
"I tried to make children not see the slain bodies on the streets," she said, adding that her children currently suffer from shock and will need treatment.
Thousands of people took matters into their own hands and, according to witnesses, left their homes in Khartoum, some in cars and others on foot, including women and children.
They said the streets were littered with dead bodies, the stench of which filled the air.
"We are now on our way to Madani to stay with our relatives after my family and kids lived through the terror of explosions," said Mohamed Saleh, 43, a government employee.
"We were very worried fighters would start storming homes."
Doctors and hospital staff describe harrowing conditions with no water for cleaning, little electricity for life-saving equipment and food running out, forcing them to send sick patients home and turn away the injured.
Many of Sudan's best hospitals are concentrated in the central Khartoum streets where the most intense fighting between the army and paramilitary Rapid Support Forces is taking place, requiring doctors and patients to brave gunfire and bombardment.
Around 320 Sudanese soldiers have fled the fighting raging in their country to neighboring Chad, the country's defense minister said Wednesday.
"They arrived in our territory, were disarmed and detained" on Sunday, General Yaya Brahim told a press conference, saying the troops feared being killed by the paramilitary Rapid Support Forces (RSF).
Meanwhile, a mission by the German military to evacuate around 150 citizens from Sudan had to be halted on Wednesday due to fighting in the capital Khartoum, the Spiegel news magazine reported citing unnamed sources.
A spokesperson for the defense ministry declined to comment on the report. The foreign ministry did not immediately reply to an emailed request for comment.
Japan was also planning an evacuation flight from Sudan for its nationals.
This report was sourced from Reuters and Agence France-Presse.