CAIRO - Israel has softened its terms for a prisoner swap with Hamas and the two are nearing a deal to exchange hundreds of jailed Palestinians for an Israeli soldier held in the Gaza Strip, officials said on Monday.

A delegation from Hamas, the Islamist group that controls the Gaza Strip, crossed into Egypt for a meeting with Egyptian security officials in Cairo to discuss the deal that Egypt and Germany have been mediating.

Officials close to the talks said Israel agreed to include in the exchange for soldier Gilad Shalit some 160 prisoners whose release it previously vetoed. But both sides have publicly avoided comment or sought to play down talk of an imminent deal.

Shalit was captured by Hamas-led gunmen who tunneled into Israel from Gaza in 2006. Israel has linked any major easing of its blockade on the territory to the soldier's return home.

The Shalit episode is about to be closed, one of the officials said.

Sources on both sides told Reuters there were hopes that a deal might be struck by the end of the week, when the Muslim festival of Eid al-Adha begins. But one Hamas official, Sami Abu Zuhri, sought to play down speculation that a deal was done.

We stress that it is premature to talk about any results regarding the prisoner swap deal, Abu Zuhri told Reuters.

In Jerusalem, Israeli officials declined to discuss in detail prospects for a deal with Hamas, a group that has rejected Western demands to recognize Israel, renounce violence and accept existing interim Israeli-Palestinian peace accords.

But Prime Minister Benjamin Netanyahu, facing questions from his rightist Likud faction in a closed-door meeting, made clear he saw no breakthrough soon and that any Palestinian prisoner amnesty would be vetted by the Israeli parliament and cabinet.

The reason that there is no discussion right now in the faction, and there is no discussion in the cabinet, is that there is no deal and no decision, Netanyahu told the lawmakers, according to an Israeli official who requested anonymity.

It is still not clear what is happening on the other side with the various demands. This will become clear with time.

SIGN OF FLEXIBILITY

Sources close to the negotiations have said Hamas, in the first part of a deal, would hand over Shalit to Egypt and Israel would release some 350 to 450 prisoners.

In a sign of flexibility from Hamas, the sources said, the group had agreed that some would go into exile rather than return to the West Bank or Gaza Strip.

More prisoners would be released when Shalit was transferred from Egypt to Israel, while other prisoner releases could take several more weeks to complete.

Officials who reported that a deal is approaching said Arabs holding Israeli citizenship are among the 160 newly agreed prisoners slated for release. Israel had objected to including Israeli Arabs in an exchange.

Public pressure has been mounting on the Netanyahu government to show flexibility in a prisoner swap, even if it meant freeing militants jailed for planning some of the most deadly Palestinian suicide bombings in Israel.

Amid the mounting speculation that a deal is near, Shalit's parents met on Monday Israel's chief negotiator in the indirect contacts with Hamas.

Of course we are hoping and want to see Gilad at home after so many years ... To my regret I cannot discuss (this) today, and I don't want to. This is not the time for chatter but for action, the soldier's father, Noam Shalit, told reporters.

On October 2, Israel freed 20 Palestinian women in return for a proof-of-life video showing the 23-year-old Shalit. (Additional reporting by Nidal al-Mughrabi in Gaza and Dan Williams in Jerusalem, Editing by Janet Lawrence)