Israel's military closed all Gaza border crossings on Saturday after announcing air strikes on Iran carried out jointly with the United States.
Israeli authorities said late on Monday they would reopen the Kerem Shalom crossing from Israel to Gaza on Tuesday, for "gradual entry of humanitarian aid" into the strip without saying how much.
Israeli authorities previously said the crossings could not be operated safely during war.
Gaza is wholly dependent on fuel brought in by trucks from Israel and Egypt and a lack of fresh supplies would put hospital operations at risk and threaten water and sanitation services, local officials say.
Most Palestinians in Gaza are internally displaced after Israel's two-year war with Hamas militants.
"Gaza is rapidly running out of its limited fuel supply ... after Israel blocked the entry of fuel and goods," said Karuna Herrmann, the Jerusalem director of the United Nations Office for Project Services, which manages fuel distribution in Gaza.
"I expect we have maybe a couple of days' running time."
Amjad Al-Shawa, a Palestinian aid leader in Gaza, who works with the UN and NGOs, estimated fuel supplies could last three or four days, while stocks of vegetables, flour and other essentials could also soon run out if the crossings remain shut.
Israel's COGAT military agency, which controls access to Gaza, said that enough food had been delivered to the territory since the start of an October truce to provide for the population.
"(The) existing stock is expected to suffice for an extended period," COGAT said, without elaborating. It declined to comment on potential fuel shortages.
The truce was part of a broader US-backed plan to end the war that involves reopening the Rafah border crossing with Egypt, increasing the flow of aid into the enclave, and rebuilding it.
Hamada Abu Laila, a displaced Palestinian in Gaza, said the closures were stoking fear of a return of famine, which gripped parts of the enclave last year after Israel blocked aid deliveries for 11 weeks.
"Why is it our fault, in Gaza, with regional wars between Israel, Iran, and America? It is not our fault," Abu Laila said.
