Ambulances took 76 seriously injured Palestinians from Gaza into Egypt on Wednesday for the first time since the war between Hamas and Israel began.
A group of 335 foreign passport holders - including British nationals - were also allowed to leave via the Rafah crossing, officials said.
Gaza's borders have been closed since Hamas's attack on Israel on 7 October.
Rafah is expected to continue opening for limited time periods to let foreign nationals and injured civilians 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, Western officials say.
The OceanNewsUK understands there are about 7,000 dual nationals in Gaza.
Speaking on Wednesday evening, US President Joe Biden said that thanks to "concerted American leadership, safe passage for wounded Palestinians and foreign nationals has started".
American citizens were able to exit, he said, as part of the first group of "probably more than 1,000", adding that the process would continue over "the coming days".
"We're working non-stop to get Americans out of Gaza as soon and as safely as possible," Mr Biden stressed.
UK Foreign Secretary James Cleverly earlier said the departure of the first of the estimated 200 Britons in the territory was "a hugely important first step".
"We are working with Egyptian and Israeli authorities to ensure the crossing stays open so all British nationals can get to safety in the coming days," he wrote on X, formerly known as Twitter.
Israel has been bombarding Gaza for more than 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.
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.
At least 76 had arrived in Egypt by the evening, according to a spokesperson for the Palestinian border authority and an Egyptian official.
"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 Palestinian border authority said 335 foreign and dual nationals had crossed by Wednesday evening.
As well as the unspecified number of Britons, they included 31 Austrians, five French nationals, four Italians and some Americans.
Médecins Sans Frontières said 22 of its international staff had successfully crossed.
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 OceanNewsUK.
"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.
Also on Wednesday, another an Israeli air strike destroyed several residential buildings in Jabalia, in northern Gaza, for the second day in a row.
Video footage and photos showed a scene of devastation in the north-western Fallujah area, with hundreds of people searching for survivors underneath rubble and shattered buildings.
The Hamas-run health ministry said dozens of people were killed or wounded in the attack.
On Wednesday night, the Israel Defense Forces (IDF) issued a statement saying its fighter jets "struck a Hamas command and control complex" in Jabalia.
"We can confirm that Hamas terrorists were eliminated in the strike," it added.
"Hamas deliberately builds its terror infrastructure under, around and within civilian buildings, intentionally endangering Gazan civilians."
The IDF also said it had been urging residents of Jabalia and other parts of northern Gaza to evacuate "to mitigate harm to civilians", as tanks and troops continue to advance from a number of directions.
On Tuesday, the IDF said a strike in the centre of Jabalia camp had killed a senior Hamas commander and "a large number of terrorists" inside "underground terror infrastructure" embedded beneath buildings. The infrastructure and buildings had collapsed as a result, it added.
Gaza's health ministry said at least 50 people were killed and 150 wounded. But a nearby hospital said it received 400 casualties, including 120 dead.
Hamas denied that the commander was dead but said seven of the hostages taken from Israel, including three foreign passport holders, were killed in the strike - a claim that could not be verified.
In a brief statement on X on Wednesday, the UN human rights office warned: "Given the high number of civilian casualties & the scale of destruction following Israeli air strikes on Jabalia refugee camp, we have serious concerns that these are disproportionate attacks that could amount to war crimes."
UN Secretary General António Guterres's spokesman also said he was "appalled over the escalating violence in Gaza" and reiterated that all parties must abide by international humanitarian law, including the principles of distinction, proportionality, and precaution.
