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Mr Mitchell will also visit the UN Office for the Co-ordination of Humanitarian Affairs.
“I thank Egypt for their sustained diplomatic efforts to get more life-saving aid into Gaza as quickly as possible," he said.
“The UK has more than doubled our aid commitment to the Palestinian people this year and we call on all parties to allow the humanitarian pauses necessary to ensure this aid reaches those in need in Gaza.”
The UK recently allocated £30 million ($37 million) in extra aid to the occupied Palestinian territories – more than doubling the existing £27 million pledged in aid this year.
The funds will help to provide Palestinians with essential humanitarian relief items such as food, water and shelter.
The latest from the Israel-Gaza war - in pictures
Three UK flights have already landed in Egypt carrying more than 51,000kg of aid since the crisis began, including items such as wound-care packs, water filters and solar-powered lights.
The government has so far ensured more than 150 British Nationals and their dependants have safely left Gaza.
The Foreign, Commonwealth and Development Office is using all channels available to it ensure any remaining registered British nationals are able to cross the Rafah border as soon as possible.
Royal Navy vessels are in the Middle East to deter further escalation.
The government continues to call on all parties to allow the humanitarian pauses necessary to allow more aid to enter Gaza.
UK Prime Minister Rishi Sunak has said that Israel’s forces must act within international law and stop extremist violence in the West Bank.
The visit to Egypt follows the G7 foreign ministers’ meeting in Japan last week.
Partners including the UK agreed in the meeting on the need for humanitarian pauses to allow urgently needed assistance, civilian movement and the release of hostages.
During Mr Sunak’s recent visit to the region, he repeated his support a two-state solution to provide justice and security for Palestinians and Israelis.