British people and other foreign nationals who have fled Gaza only have 72 hours - three days - in Egypt before they need to leave.
Hundreds of foreign nationals were evacuated from Gaza into Egypt through the Rafah Crossing on Friday.
The border was then closed all weekend.
The Foreign, Commonwealth and Development Office (FCDO) said: "We remain in contact with British nationals in the region to provide them with the latest information."
It added in a statement that it was "using all diplomatic channels to press for the crossing to reopen in coordination with our international partners".
Nasser Alshanti, an academic from Manchester, told BBC News his pregnant daughter Yosra is effectively "stuck" in Egypt because her husband isn't a British citizen, and are worried they won't be able to leave before the three days are up.
Yosra was raised in the UK and moved to Gaza for university in 2015, where she met - and then married - Ibrahim. The couple had lived in central Gaza since then, until they had to flee in the first week of the war when their neighbourhood was bombed.
They were evacuated from Gaza into Egypt via the southern border crossing at Rafah at the end of last week, and are now in Cairo.
Because Ibrahim is not a British national, they now need to apply for a Family Visa for him before they can travel to the UK.
But the 72-hour deadline in Egypt means they are worried about overstaying if they don't get a visa in time. Under current rules, overstaying would mean having to pay a fine, which could be greater the longer they stay.
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"I thought they would give him an emergency visa or something, a very quick visa just to evacuate them from Cairo before the end of the 72 hours," Dr Alshanti said.
A British Family Visa application submitted outside the UK normally takes up to six months to process.
The FCDO and Home Office are working together to approve visas for non-British family members of British people who've been evacuated from Gaza, with a sped-up process that they expect to be much quicker than usual. However, it's not yet known how long this will take.
Dr Alshanti said that sheltering in Gaza in the last few weeks, and now the stress of being in limbo in Egypt, has taken its toll on his daughter.
"I've just done a video call with her," he said. "You can tell from her face how much weight she's lost. The last time I saw Yosra was in August, which was just three months ago - but she's totally different. You can see how her eyes [are sunken] and her face is quite pale.
"For a heavily pregnant lady, after three weeks in a shelter with a small amount of food and water and no electricity - what do you expect?"