The political leader of Palestinian militant group Hamas has said it is willing to take a serious step towards peace if Israel does the same.
Khaled Meshaal told the BBC that Hamas would not renounce violence, saying resisting an occupation was legal.
But he said a long-term truce would be possible if Israel accepted conditions including a return to its 1967 borders.
Israel's acting PM said if he won next month's poll, Israel would retain West Bank settlement blocs and Jerusalem.
However, Ehud Olmert said Israel would be prepared to give up parts of the West Bank where most Palestinians were living.
His interview on Israel television was his first since taking power a month ago following Ariel Sharon's massive stroke.
Mr Meshaal said he wanted to send a message to the next Israeli government that Hamas would be ready to talk if Israel met certain strict conditions.
The most important of these was that Israel must withdraw to the boundaries it had until the 1967 Middle East war, Mr Meshaal told the BBC's Middle East editor Jeremy Bowen.
Hamas would then "possibly give a long-term truce with Israel", he said.
"This is a position that Hamas could take, but not now, only after Israel recognises the rights of the Palestinians, to show and confirm its willingness to withdraw to the 1967 borders," he said.
Mr Meshaal said such a move by Israel could create conditions for the international community to find a solution for all of the region's problems.
Our correspondent says that by putting the onus on the international community, the Hamas leader seems to be displaying a willingness to accept international mediation.
But Mr Meshaal, who lives in exile in the Syrian capital, Damascus, also warned that the militant group was capable of leading the Palestinians in a long fight that they would be better able to bear than Israel.
He and other Hamas leaders are in the Egyptian capital, Cairo, to discuss the next step after their 25 January election win over rivals Fatah.
Hamas has largely observed a truce in its fight with Israel for the past year.
However, Israel believes offers like the latest by Mr Meshaal are a ruse to allow Hamas to gather its strength, since its charter calls for the destruction of the Jewish state, our correspondent says.
Speaking on Channel 2 TV, Mr Olmert said Israel would retain "united Jerusalem", which would include occupied East Jerusalem, if his Kadima party won Israel's general election on 28 March.
But he said Israel would disengage from parts of the West Bank where the population is mostly Palestinian, at the same time as retaining its three main settlement blocs.
Israel has occupied East Jerusalem since 1967. It annexed the area in 1981 and sees it as its exclusive domain.
Under international law the area is considered to be occupied territory.
East Jerusalem is often called Arab East Jerusalem because the majority of its residents are Palestinian, and Palestinians hope to establish their future capital there.