But the United Nations dismissed a Saudi demand that tighter inspections be put in place at Yemen's rebel-held Hodeida port before a devastating blockade is lifted.
"If we don't have the fuel to deliver our supplies to millions of starving Yemeni families, we will continue to witness more children dying of hunger", Muhrez said.
Saudi Arabia and its allies tightened a longstanding blockade of Yemen's land, sea and air borders a week ago in response to a missile fired by the Iran-backed Huthis that was intercepted near Riyadh global airport.
Yemen used to import about 70 percent of its daily needs before the blockade, but since the start of the siege, food and medicine are in short supply, with cooking gas prices having surged by around 100 percent and fuel unavailable at most gas stations.
The top United Nations aid official in Yemen called on the Saudi-led coalition on Tuesday to open all Yemen's sea ports urgently, saying it risked damaging the fight against cholera and hunger, with 7 million already in "famine-like conditions".
"There is no embargo", Ambassador Abdallah Al-Mouallimi said.
Saleh al-Sammad, the head of the Presidency Council of Yemen's rebels, also known as Houthis, told a rally of thousands of supporters marching down a main boulevard in the capital, Sanaa, that the coalition has "shut down all doors for peace and dialogue". According to the UN's aid coordinator in Yemen, Jamie McGoldrick, there was no time to wait for a new inspection system to be set up.
Saudi Arabia announced Monday that the Saudi-led coalition fighting Shiite rebels in Yemen will begin reopening airports and seaports in the Arab world's poorest country, days after closing them over a rebel ballistic missile attack on Riyadh. The announcement has come after the coalition and their allies have faced severe criticism internationally over the closure.
Those ports are in Yemeni cities of Aden, Mocha and Mukalla.
The coalition said on Monday it would re-open ports in areas held by allied forces. More than two-thirds of the people in need and 80 per cent of all cholera cases in Yemen are closest to the two ports, which are both in rebel-held territory. Houthis, on the other hand, have denied the allegation.