GAZA, May 13 (Reuters) - Israel and the Palestinians were close to reaching a deal on Sunday that would end the hunger strike of more than 1,000 Palestinian prisoners, a Hamas spokesman and a Palestinian official said.

We hope the intensive efforts by Egypt (mediators) to meet the prisoners' demands will reach a positive conclusion in the coming hours, said Taher al-Nono, spokesman of the Hamas government in Gaza.

An Israeli Prisons Service spokeswoman would not confirm nor deny that an Egyptian-mediated deal had been reached. An Israeli government spokesman declined to comment on the matter.

A Palestinian official who is close to the talks said the deal may be brought before the prisoners as early as Monday.

A deal could be reached tonight, but it should be presented to prisoners in the Israeli jails, possibly Monday morning, for endorsement before an official announcement, said the official, who was speaking under condition of anonymity due to the sensitivity of the issue.

An Egyptian official close to the talks said the deal had not yet been finalized.

An estimated 1,600 Palestinian inmates out of 4,800 in Israeli jails launched the hunger strike on April 17 to demand improved conditions in Israeli custody, such as an end to solitary confinement and more family visits.

They have also challenged Israel's policy of indefinite detention without charge of suspected Palestinian militants.

Israel says all prisoners receive adequate medical attention, including in civilian hospitals if required.

Defending its so-called administrative detention policy, Israel says some cases cannot immediately be brought to open court for fear of exposing Palestinian intelligence sources that have cooperated with Israeli security organs against militants.

The prisoners include militants from Islamist Hamas and Islamic Jihad, which reject peace with the Jewish state, as well as members of Palestinian President Mahmoud Abbas's secular and Western-backed Fatah movement.

Two inmates who helped launch the hunger strike, Bilal Diab and Thaer Halahla of Islamic Jihad, were in the 76th day of their fast on Sunday. (Reporting by Nidal al-Mughrabi; Writing by Maayan Lubell Editing by Maria Golovnina)