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The leader of the Scottish National Party piled pressure on Foreign Secretary James Cleverly to use positive British-Israeli relations to push for civilians in the densely populated Palestinian territory to be given safe passage out.
Gaza is under an Israeli air, sea and land blockade.
In a letter to Mr Cleverly on Tuesday, Mr Yousaf appealed to him to intervene in a bid to persuade Israel’s government to open a humanitarian corridor.
“Too many innocent people have already lost their lives as a consequence of these completely unjustifiable and illegitimate attacks by Hamas,” Mr Yousaf wrote.
“However, innocent men, women and children cannot, and should not, pay the price for the actions of a terrorist group.”
He spoke on Monday about how his wife's parents were stuck in Gaza after a visit to her 93-year-old grandmother.
“As a close friend and ally of Israel, I therefore ask the UK government to call on the government of Israel to ensure innocent civilians are protected, and to put in place an immediate ceasefire to allow the safe passage of civilians through the Rafah border,” he said in his letter.
Israeli air strikes and artillery hit the area near the Rafah border crossing between Gaza and Egypt on Tuesday, Egyptian officials said. It was the third in 24 hours.
Explosions on Monday forced authorities to suspend operations.
The crossing is the only one in Gaza not controlled by the Israeli authorities and the sole exit route for 2.3 million Palestinians living in the strip.
Mr Yousaf also called for essential supplies to be taken into Gaza, after Israel's Defence Minister Yoav Gallant ordered a “complete siege” on the territory, saying Israeli authorities would cut electricity and block the entry of food, water and fuel.
The Scottish National Party leader, born in Glasgow to Pakistani immigrants, said Israel “should open a humanitarian corridor into Gaza to allow supplies, including food, fuel, water and medical supplies, for those civilians who are trapped, helpless and cannot leave.”
Mr Yousaf's wife said she feels like she is “just living in a nightmare” after her parents became trapped.
Nadia El-Nakla told the BBC that her parents, Elizabeth and Maged El-Nakla, “continually” tell her “they feel like they are going to die”.
“There is no electricity from 2pm their time, which was just a few hours ago," she said. "No electricity means no hospital supplies, it means no food. You can’t even preserve the food that you have.
“I don’t know what it means for them in the long-term, I don’t know what’s about to happen to them.
“For me, my number one is my family being safe.”
Hamas’s large-scale attack on Israel, launched in the early hours of Saturday, left more than 1,200 people dead, including about 260 young revellers at the Supernova music festival near the Gaza border.
Israel has responded by striking Hamas targets in Gaza, killing more than 1,000 people.
Mr Yousaf’s call came as Irish Prime Minister Leo Varadkar urged Israel to show “restraint” in its response to Hamas’s attacks.
“From Ireland’s point of view, we are saying to Israel that yes you have a right to defend yourself, you’re surrounded by enemies who want to end your existence, but any response must be proportionate,” Mr Varadkar told the Irish broadcaster RTE.
He said while there is “a lot of solidarity internationally for Israel at the moment”, there is a risk that this could “fall apart if Israel goes too far in terms of its actions in Gaza".
“There’s a risk then of violence flaring up in the West Bank, in Lebanon and other places so we’re very much calling for restraint,” Mr Varadkar said.
Israeli Prime Minister Benjamin Netanyahu warned the bombardment was “only the beginning” of his military’s response to the terrorist assault.
Antony Blinken, the US Secretary of State, is expected to visit Israel later on Wednesday.