More than a thousand Palestinian prisoners went on a hunger strike to press for better conditions, but Israel responded by tightening inmate restrictions, and a Cabinet minister said he wouldn't care if they starved to death.

About 1,600 prisoners struck on Sunday. Organizers say the rest of the 7,500 detainees are to join by the end of the week to press for greater access to phones, an end to strip searches and more family visits. Many prisoners have not seen their families because an Israeli security closure bars Palestinians from Israel.

In the past four years, Israeli troops have rounded up thousands of Palestinians on suspicion they were involved in bombing and shooting attacks that have killed nearly 1,000 Israelis. The prisoners are being held in Israeli jails, a large tent camp in the Negev Desert and at crowded military bases in the West Bank, where prisoners have complained of poor sanitary conditions.

The strike was organized by the main Palestinian factions — Hamas (search), Islamic Jihad (search) and Fatah (search). The Palestinian government said it backed the prisoners and declared Wednesday a day of solidarity.

"We fully support the legitimate demands of the prisoners and the ending of the policy of collective punishment, torture and terror by the Israeli prison administration against the prisoners and their families," Palestinian Prime Minister Ahmed Qureia (search) said in a statement.

Israeli officials imposed additional restrictions — including banning all family visits and the sale of cigarettes and candy. "At this point, the security prisoners are refusing their meals and they are drinking water," said prison services spokesman Ian Domnitz.

Israeli Public Security Minister Tzachi Hanegbi said over the weekend Israel would not give in to the prisoners' demands. "The prisoners can strike for a day, a month, even starve to death, as far as I am concerned," Hanegbi said.

In violence in Gaza, Israeli helicopters fired four missiles north of Gaza City near the border with Israel early Monday, witnesses said. Two people were killed, Palestinian hospital officials said.

Israeli military sources, speaking on condition of anonymity, gave a different account. They said soldiers spotted militants setting up a rocket launcher, and the helicopters targeted them, hitting one. Ambulances arrived at the scene but hesitated to enter because of Israeli gunfire, witnesses said.

As the hunger strike began, the most prominent Palestinian prisoner, who also was participating in the protest, was planning out ways to ease the transition in the Gaza Strip after Israel's planned withdrawal next year, according to a document obtained Sunday by The Associated Press.

Marwan Barghouti, a leader of Yasser Arafat's (search) Fatah movement, has presented an 18-point plan for Gaza to Hamas and Islamic Jihad, and the leaders of the two militant groups responded "positively, in principle," according to a source close to Barghouti.

Islamic Jihad spokesman Mohammed al-Hindi, however, said the group had not received the document or had any contact with Barghouti. Al-Hindi said he suspected the report had been fabricated by Israel "to measure the reactions of the Palestinian factions regarding important items, including our holy right to fight the occupation."

There was no immediate reaction from Hamas.

Barghouti proposed that after the Israeli withdrawal, militant groups be given a role in running Gaza, but insisted that they halt attacks on Israel from that territory — though not from the West Bank.

Since Israel announced its pullout plan, concerns have been raised about a power vacuum and a possible takeover by Islamic militants. Under Barghouti's plan, Arafat's Palestinian Authority would be the sovereign in Gaza, but a "monitoring committee" with representatives from all groups would have considerable say.

Barghouti, seen as a possible successor to Arafat, is serving five consecutive life terms for a role in attacks that killed five people, but is frequently mentioned in reports about possible prisoner exchanges.

The issue of prisoners is especially sensitive to Palestinians. Though it is not mentioned in the U.S.-backed "road map" peace plan, initial efforts to implement the plan last year bogged down, in part, over the release of Palestinian prisoners. Israel set free a few hundred, but Palestinians complained most were common criminals near the end of their terms.