JERUSALEM — Egyptian and Palestinian officials said Sunday they were close to reaching a deal with Israel that would end a mass hunger strike by Palestinians in Israeli jails.

Some 1,600 Palestinian prisoners are on strike, most for a month, but three have refused food for more than 70 days. They launched the strike to press their demands for better conditions and an end to detention without trial.

An Egyptian-drafted proposal calls for Israel to move prisoners currently held in solitary confinement to regular cells, and allow families from Hamas-ruled Gaza to leave the seaside strip to visit imprisoned relatives, an Egyptian official said on condition of anonymity because of the sensitivity of the discussions.

It also calls for Israel to ease a policy called "administrative detention" under which some prisoners deemed a security risk can be held indefinitely without charge. Under the draft agreement, that policy would be changed and prisoners will be either charged or released after they are detained.

Palestinian prisoners have yet to review the proposal, and Israeli officials refused comment.

A Palestinian lawyer representing the prisoners confirmed the details of the proposal, and said Egyptian officials had presented it to the Israelis.

Taher Nunu, the spokesman for the Hamas government in Gaza, said Egyptian mediation efforts were under way, and that he hoped "for an answer within hours" from the prisoners to the proposal.

While the existence of a draft proposal is a significant step forward, it may still face serious obstacles before Israeli officials and Palestinian prisoners agree to a deal.

Still, both sides need to show results. Israel faces the specter of mass demonstrations, and potential violence, when thousands of Palestinians take to the streets Tuesday to commemorate their defeat in the 1948 war surrounding Israel's independence.

The leaders of the Palestinian hunger strikers need to show their people that the nonviolent protest can produce results.

Two of the prisoners staging the longest strike, Thaer Halahleh and Bilal Diab, are members of Islamic Jihad, a violent Palestinian militant group that has killed hundreds and injured many more in suicide bombings, shootings and other attacks. It is not clear whether they were involved in violence or not.

According to prison officials, at least 1,600 of the 4,600 Palestinians held by Israel are refusing food. Palestinians say about 2,500 prisoners are taking part in the hunger strike.

Many of the Palestinians striking have been convicted of involvement in deadly attacks against civilians. Others, including the longest-striking prisoners, are being held without charge, including Halahleh and Diab.

Israel's prisons service says the hunger strikers are under constant medical supervision and are in stable condition.