Egypt's military on Thursday said three of its aircraft brought home its troops stranded in northern Sudan after fighting broke out between the Sudanese army and the Rapid Support Forces paramilitary.
Servicemen captured by the RSF, meanwhile, have been released and taken to the Egyptian embassy in Khartoum.
A statement by the armed forces' spokesman did not say how many men were in each group, but the Sudanese military on Wednesday said 177 Egyptian air force personnel has been flown to Egypt from the northern Sudanese town of Dongola.
It put the number of troops at the Egyptian embassy at 27.
Egypt's Foreign Ministry said the release and transfer of soldiers to the embassy was carried out with "the co-ordination and co-operation" of the UAE.
"The two countries expressed their appreciation of the efforts made by the International Red Cross in support of securing the safety of the Egyptian soldiers," the ministry said.
An identical statement by the UAE also cited co-operation between the two Arab allies and emphasised their "commitment to continue efforts to stop the fighting in Sudan, protect civilians and allow the resumption of dialogue between Sudanese stakeholders to resolve their differences, proceed to a transitional stage and eventually arrive at the hoped-for security and stability in Sudan".
Fighting in Khartoum between the army and the RSF was continuing for a sixth day on Thursday after several failed attempts at a ceasefire.
The Egyptian military said the soldiers at the embassy would be flown home "as soon as conditions stabilise and security circumstances permit".
The military personnel were captured when the RSF overran an army base in northern Sudan last weekend. The RSF on Wednesday said it had taken the men to Khartoum.
Thursday's Egyptian military statement said the 177 men who were flown home had not been captured by the RSF, contrary to the Sudanese military's claims.
Egypt said its soldiers were taking part in a training mission under a military protocol signed with Sudan and denied that it was taking sides in the conflict.
A video clip posted online last week showed RSF fighters forcing a small group of Egyptian soldiers to crawl on their stomachs. An RSF member was seen hitting one of the soldiers and heard abusing them.
The clip triggered an outcry in Egypt, with social media users voicing their anger and demanding retribution.
President Abdel Fattah El Sisi's government forged close military ties with Sudan following the removal from power in 2019 of former president Omar Al Bashir.
Relations between Cairo and Khartoum were often fraught during Al Bashir's 29-year rule.
The neighbours have frequently held joint war games over the past three to four years.
Egypt has traditionally viewed its neighbour to the south as an extension of its national security sphere.
However, its latest efforts to establish close relations with Khartoum were in part motivated by Cairo's wish to put pressure on Ethiopia, which is building a dam on the Nile that Egypt says could compromise its vital share of the river's water.
Sudan's army chief Gen Abdel Fattah Al Burhan has visited Egypt at least three times since Al Bashir's removal and was given a head-of-state reception, complete with a guard of honour, on a visit last year.
In contrast, RSF commander Gen Mohamed Dagalo, has visited once in the same period.
Mr El Sisi, a former army general, this week reviewed the conflict in Sudan with his top commanders, saying later in televised comments that Egypt was prepared to mediate and that his government was in contact with the warring sides.
