Plumes of smoke rose on Thursday over the northern Gaza Strip, where Israel's military urged civilians to evacuate, as rescuers said Israeli strikes across the territory killed more than 50 people.
Gaza's civil defence agency said there had been "52 martyrs and dozens injured as a result of air strikes carried out by the occupation" across the territory on Thursday.
The latest evacuation warning for parts of Gaza City and neighbouring areas came hours after the United Nations said it had begun distributing around 90 truckloads of aid in Gaza, the first such delivery since Israel imposed a total blockade on 2 March.
Under global pressure to lift the blockade and halt a newly expanded offensive, Israeli Prime Minister Benjamin Netanyahu said he was open to a "temporary ceasefire", but reaffirmed the military aimed to bring all of Gaza under its control.
In an Arabic-language statement on Thursday, the military said it was acting "with intense force" in 14 areas of the northern Gaza Strip, including parts of Gaza City and the Jabalia refugee camp.
A map posted alongside the warning showed a swath of territory marked in red, with the army accusing "terrorist organisations" of operating there and urging civilians to move south.
The army issued a similar evacuation call for northern Gaza late Wednesday in what it said was a response to rocket fire.
The vast majority of Gaza's 2.4 million have been displaced at least once during the war.
After Israel announced it would allow in limited aid, the United Nations "collected around 90 truckloads of goods from the Kerem Shalom crossing and dispatched them into Gaza", said Stephane Dujarric, spokesman for UN chief Antonio Guterres.
In Gaza, the Gaza government media office reported the arrival of 87 aid trucks, which it said were allocated to international and local organisations to meet "urgent humanitarian needs".
Netanyahu said it was necessary to "avoid a humanitarian crisis to preserve our freedom of operational action".
Palestinians have been scrambling for basic supplies, with Israel's blockade leading to critical food and medicine shortages.
There was no comment from the Israeli military on any strikes on Thursday.
UN agencies have said that the amount of aid entering Gaza falls far short of what is required to ease the crisis.
AFP footage showed bags of recently delivered flour at a bakery in the central city of Deir el-Balah, where workers and a host of machines began kneading, shaping, baking and packaging stack after stack of pita bread.
"Some aid is finally reaching Gazans in desperate need, but it's moving far too slowly," said Cindy McCain, executive director of the World Food Programme.
The amount is still a "tiny drop in the bucket" compared to the scale of the crisis, she said.