Six Israeli human rights groups have appealed to the High Court of Justice, demanding that Israel allow essential supplies into the Gaza Strip.
More than half Gaza's population receives UN food aid
The Israeli military is conducting an offensive in Gaza following the capture of one of its soldiers two weeks ago.
A spokesman for the groups said that withholding food, fuel and essential equipment was collective punishment in violation of international law.
Israel has allowed brief openings of the main goods crossings into Gaza.
But lengthy closures have made the already dire humanitarian situation worse.
The UN has 230 containers of food waiting to pass through the Karni cargo crossing between Israel and Gaza, which has been closed since Monday, officials say.
Before the offensive, UN aid relief workers were giving daily food rations to 735,000 Gazans, more than half the overcrowded territory's population of 1.4m people.
Frequent closures are justified by Israel on security grounds - crossing points are the only place where Palestinian militants can get close enough to Israeli troops to launch guerrilla attacks.
The groups' petition to the high court also demands that Israeli force stop attacking civilian targets such as bridges and power stations.
"Israel is required... by law to discern at all times between military and civilian targets, to avoid attacking obvious civilian targets such as power stations and to participate actively in supplying the basic needs of the civilian population," the petition says.
The European Union has started delivering emergency fuel supplies to public hospitals in Gaza.
Hospitals are having to use generators, after the Israeli army attacked the main power plant.
Israeli bombing has destroyed some of Gaza's infrastructure
They are the first supplies to be sent through a temporary funding mechanism set up by the Quartet group of mediators in the Middle East conflict - the EU, United Nations, United States and Russia.
The Palestinian government has welcomed the aid but said the EU was undermining Palestinian democracy by bypassing the Hamas-led administration.
Western donors refuse to send direct aid to the government until Hamas renounces violence and recognises Israel.
European officials say a second delivery of aid will begin in the next few days, paying cash allowances directly to Palestinian health workers who have not been paid for four months.
In addition to more than 50 Palestinians killed by military action, a number of deaths have occurred among more than 500 people stranded at the Rafah crossing between Gaza and Egypt.
Egyptian health officials said an 18-month-old Palestinian boy died from heat stroke on Tuesday, as well as a 19-year-old woman waiting to return to Gaza after undergoing surgery in Egypt.
The crossing has been closed by Israel since the capture of Cpl Gilad Shalit on 25 June to prevent the soldier being smuggled into Egypt, Israeli officials say.