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In a phone conversation Sheikh Mohamed and Mr Guterres emphasised the need to intensify diplomatic efforts to open critical humanitarian corridors and establish a ceasefire to enable the delivery of relief and medical aid, state news agency Wam reported on Wednesday evening.
The two men underscored the need to adhere to international law on the protection of civilians, in light of the escalating violence.
"The two sides also emphasised the importance of urgent action to halt escalation and enable diplomatic efforts to contain the situation and restore calm," reported Wam.
"They also highlighted the grave potential repercussions of the crisis on regional peace, stability, and security."
The discussion covered the role of the UN and other key international stakeholders in finding a "comprehensive, just and lasting peace" between Israel and Palestine, to achieve security and stability in the region.
The phone call came as tensions continue to grow following the strike on Al Ahli Arab Hospital in Gaza that killed about 500 civilians on Tuesday.
US President Joe Biden was in Tel Aviv on Wednesday where he said his top priority remained the release of Israeli prisoners held by Hamas.
"I have come to Israel with a simple message: You are not alone," he said.
"As long as the United States stands – and we will stand forever – you will not be alone."
His remarks came as the number of Palestinian deaths rose to more than 3,400. The number of Israelis killed is about 1,400.
As the crowds moved away from Al Manara Square, in the middle of the occupied West Bank’s administrative capital, chants of “America equals terrorist” and other anti-West slogans were heard.
The Israeli military has denied responsibility for the strike.