Two Israeli cabinet ministers have said the government should examine any serious ceasefire proposal from the Palestinian Islamist group Hamas.
Mr Ben Eliezer said recognition of Israel was not vital to talks
Infrastructure minister Binyamin Ben-Eliezer and transport minister Shaul Mofaz say offers of a truce should be given serious consideration.
Israel refuses to negotiate until Hamas, which controls the Gaza Strip, recognises its existence.
But Mr Eliezer said this should not be a precondition for talks to take place.
"If Hamas comes to us with a serious proposal for a long-term truce, in my opinion Israel should not reject it," Mr Ben-Eliezer told Israeli public radio on Friday.
"For that, it would not be vital for Hamas to recognise Israel first."
"What is essential is that it stop rocket fire and all other attacks against Israel from Gaza and that it agrees to stop arms smuggling on the Egypt border," Mr Ben-Eliezer said.
He also linked any dialogue with the release of an Israeli soldier, Gilad Shalit, who was captured by Palestinian militants in June last year.
On Wednesday, transport minister Shaul Mofaz suggested that Israel should consider talking to Hamas through a third party.
Mr Ben-Eliezer and Mr Mofaz were responding to reports that Hamas had delivered proposals for a truce to end rocket attacks by militants and Israeli military operations Gaza.
The office of the Israeli Prime Minister, Ehud Olmert, said it had not received any messages regarding a truce.
A spokesman for Mr Olmert reiterated that Israel would not deal with Hamas until it accepted three conditions: recognising Israel, renouncing violence and accepting past peace accords.
Hamas has always refused to do this.