It has accused UN agencies of not picking up aid at the borders and delivering it.
The joint statement also demanded an end to the use of lethal force near aid distribution sites and lorry convoys, where the UN says more than 1,300 Palestinians have been killed, mostly by the Israeli military.
Separately, the World Health Organisation on Tuesday appealed to Israel to let it stock medical supplies to deal with a “catastrophic” health situation before it seizes control of Gaza City.
“We all hear about ‘more humanitarian supplies are allowed in’ – well it’s not happening yet, or it’s happening at a way too low a pace,” said Rik Peeperkorn, the agency’s representative in the Palestinian territories.
“We want to as quickly stock up hospitals,” he added. “We currently cannot do that. We need to be able to get all essential medicines and medical supplies in.”
Israel’s war cabinet voted on Monday to occupy Gaza City, a move condemned at an emergency meeting of the UN Security Council later that day. On Tuesday the Israel Defense Forces (IDF) said it was “at the beginning of a new state of combat”.
The Israeli government has not provided an exact timetable on when its forces would enter the area. On Sunday, Prime Minister Benjamin Netanyahu said Israel’s forces had been instructed to dismantle the “two remaining Hamas strongholds” in Gaza City and a central area around al-Mawasi.
He also outlined a three-step plan to increase aid in Gaza, including designating safe corridors for aid distribution, as well as more air drops by Israeli forces and other partners.
On the ground, however, residents of Gaza City said they had come under unrelenting attack from the air. Majed al-Hosary, a resident in Zeitoun in Gaza City, told AFP that the attacks had been “extremely intense for two days”.
“With every strike, the ground shakes. There are martyrs under the rubble that no one can reach because the shelling hasn’t stopped,” he said.
“It sounded like the war was restarting,” Amr Salah, 25, told Reuters. “Tanks fired shells at houses, and several houses were hit, and the planes carried out what we call fire rings, whereby several missiles landed on some roads in eastern Gaza.”
The Hamas-run health ministry in Gaza said that 100 dead had been brought to hospitals across Gaza over the past 24 hours, including 31 people who were killed at aid sites. Five more people had also died of malnutrition, it added.
Israel has faced mounting criticism over the 22-month-long war with Hamas, with UN-backed experts warning of widespread famine unfolding in the besieged territory.
On Tuesday members of an international group of former leaders known as “The Elders” for the first time called the war in Gaza an “unfolding genocide” and blamed Israel for causing famine among its population.
Following a visit to the Gaza border, Helen Clark and Mary Robinson, a former prime minister of New Zealand and a former president of Ireland, said in a joint statement: “What we saw and heard underlines our personal conviction that there is not only an unfolding, human-caused famine in Gaza. There is an unfolding genocide.”