RAMALLAH, West Bank, Oct 3 (Reuters) - Hundreds of Palestinians in Israeli jails have joined a hunger strike to protest against worsening prison conditions, the Palestinian minister for prisoner affairs said on Monday.

Issa Qaraqea told Reuters that some 500 prisoners in Israeli jails were refusing to eat, rapidly swelling the ranks of the protest which began last week.

The strike was called after Israeli Prime Minister Benjamin Netanyahu toughened restrictions on Palestinian prisoners as part of an effort to force the Islamist group Hamas to free a kidnapped Israeli soldier.

Gilad Shalit was seized by Palestinian militants just outside the Gaza Strip in 2006 and Hamas, which governs the tiny coastal territory, is seeking the release of more than 1,000 Palestinian prisoners in return for his freedom.

Sivan Weizman, a spokeswoman for Israel's Prisons Service, said only 160 prisoners were on a hunger strike and that some of them stopped eating six days ago.

They are all under medical supervision and none is in danger, she said, adding that they were all drinking water.

Around 6,000 Palestinians are detained in Israeli prisons, according to Qaraqea, who said that most of those not on the open-ended strike were nonetheless shunning food for three days every week in solidarity with the others.

Thousands of Palestinians staged rallies in both the Gaza Strip and the occupied West Bank on Monday to voice their support for the protest.

Freedom can only be complete when the homeland is liberated and prisoners are released, chanted protesters in Ramallah.

Israel has agreed in principle to a prisoner swap but there is no agreement on who should be released.

Netanyahu announced in June that Palestinians would see curbs on their prison rights until Shalit was handed over.

Rights groups said the clampdown included preventing access to books, educational programmes and new clothes, expanding solitary confinement, cutting back on family visits and forcing detainees to meet their lawyers with their hands cuffed.

A senior Hamas official warned that rather than bow to Israeli pressure, militants would abduct more Israeli soldiers to push their demand for a mass-release of Palestinian inmates.

More of Shalit's kind are coming, Hamas lawmaker Ismail Al-Ashqar said in Gaza, adding that the effort to kidnap soldiers will continue until prisoners are freed. (Reporting by Nidal Almughrabi and Ali Sawafta; Editing by Marwa Awad)