Ambulances carrying seriously injured Palestinians have crossed from Gaza into Egypt for the first time since the war between Israel and Hamas began.
At least 320 foreign passport holders have reportedly also been allowed to leave via the Rafah crossing.
Gaza’s borders have been closed since Hamas’s attack on Israel on 7 October.
Western officials say Rafah is expected to continue opening for limited time periods to allow foreign passport holders and injured civilians to leave.
The lists of those allowed to cross will be agreed between Egypt and Israel, with embassies from the relevant countries being informed in advance to ensure they can prepare to receive their citizens, according to the officials.
The BBC understands there are about 7,000 dual nationals in Gaza.
UK Foreign Secretary James Cleverly said British consular officials were ready to assist the estimated 200 Britons as soon as they were able to leave.
Israel has been bombarding Gaza for more three weeks and has recently sent in ground forces in response to an unprecedented cross-border assault by Hamas gunmen in which 1,400 people were killed and 240 taken hostage.
Gaza’s health ministry says more than 8,700 people have been killed in the territory since then, while the UN says supplies of food, water, fuel and medicine are dangerously low because of a siege imposed by Israel.
Map of Gaza showing the zone in the north which Israeli authorities have ordered civilians to evacuate by moving south of the Wadi Gaza.
Ambulances were seen rushing to Rafah on Wednesday morning. At least two children were among the wounded – one with a bandaged stomach. After medical checks, they were carried away on stretchers.
The BBC’s Rushdi Abu Alouf, who is at the crossing, was told by Palestinian passport control officers that 88 patients requiring advanced medical treatment were expected to be transferred to Egypt.
At least 76 had arrived in Egypt by late afternoon, an Egyptian official told AFP news agency.
“Hospitals in the Gaza Strip are treating large numbers of injured people while suffering from a lack of medical supplies. Therefore [they] cannot operate on such cases,” Nassem Hasan, a medic working with Gaza’s health ministry, told Reuters news agency.
“Now they are being transported to the Egyptian side, and will then be evaluated and might be relocated to another hospital.”
Most of the patients will be taken to a field hospital built by Egyptian authorities in Sheikh Zuweid, 15km (9 miles) from Rafah. Others will go to permanent hospitals in the nearby town of El-Arish or the city of Ismailia.
The director general of the World Health Organization, Tedros Adhanom Ghebreyesus, welcomed Egypt’s decision to accept medical evacuations.
But he warned: “Attention must not be diverted from the far greater needs of thousands of patients in Gaza, many of them extremely fragile who cannot be moved.
“We need an immediate acceleration in the flow of medical aid permitted into Gaza. Hospitals must be protected from bombardment and military use.”
The WHO says more than a third of Gaza’s hospitals are not functioning, while the rest are only partly working and are overwhelmed by casualties.
Gaza’s health ministry says more than 20,000 people have been injured.
The temporary opening of the crossing comes amid a worsening humanitarian crisis in Gaza.
Our correspondent said about 500 foreign and dual nationals were also expected to be allowed to cross into Egypt on Wednesday.
In the afternoon, Egyptian state-run Al-Qahera News TV broadcast footage showing what it said was the first group getting off a coach, which included many women and young children.
Mohammed Ghalayini, a British scientist from Manchester who had been in Gaza visiting family when the war began, accompanied his uncle to the crossing after he was named by Gaza authorities on the list of potential evacuees.
“People are really afraid of what’s going on and so if they have a chance to leave, they’re trying to leave,” he told the BBC.
“But getting to the border is a struggle as well, because fuel supplies are short,” he added. “So you know, I saw people arriving on a donkey cart with their luggage at the border.”
Other British nationals hoping to cross in the coming days include the parents-in-law of Scottish First Minister Humza Yousaf.
He welcomed news that the border was opening up, but said his in-laws were trapped without clean drinking water and with rapidly diminishing supplies.