According to international media reports, evacuation flights were continuing early Monday, with hundreds of people flown out overnight on military aircraft.
Foreigners also fled the capital Khartoum in a long United Nations convoy, while millions of frightened residents hunkered down inside their homes, many running low on water and food.
Across the city of five million, army and paramilitary troops have fought ferocious street battles since April 15, leaving behind charred tanks, gutted buildings and looted shops.
More than 420 people have been killed and thousands wounded, according to UN figures, amid fears of wider turmoil and a humanitarian disaster in one of the world’s poorest nations.
US special forces launched a rescue mission Sunday for around 100 embassy staff and their relatives, swooping in with Chinook helicopters to fly them to a military base in Djibouti.
US forces “will remain deployed in Djibouti to protect United States personnel and others until the security situation no longer requires their presence”, President Joe Biden said Sunday in a letter to the Speaker of the House.
British Prime Minister Rishi Sunak said UK forces had also rescued diplomats and their families while Canadian Prime Minister Justin Trudeau said his country had temporarily suspended its evacuation operation.
“Our diplomats are safe – they have been extracted and are working from outside the country,” Trudeau tweeted.
Germany and France meanwhile said they had also begun evacuating their nationals and those from other countries.
Two French planes carrying around 200 people of multiple nationalities landed in Djibouti.
Nearly 1,000 Turkish citizens set out for home from two points in the capital Khartoum and another point from Wad Madani city, according to Turkish media.
The German army said it had evacuated 101 people on the first of three military aircraft sent to Sudan.
The first Airbus A400M “landed safely in Jordan” at around midnight local time (2100 GMT Sunday), the Bundeswehr said on Twitter. Another plane with 113 people was on its way to Jordan, it said.
Italy evacuated about 300 people in total, according to their foreign ministries.
Ireland said it was also dispatching an emergency team to assist with evacuating its citizens and their dependants.
Egypt, Sudan’s large neighbour to the north, said it had evacuated 436 nationals by land.