Hamas has offered total ceasefire if Israel agrees to persuade the international community to lift economic and political boycott of the Palestinians following the formation of the unity government.
The Palestinians "will offer a promise from Hamas and Fatah of a total ceasefire with Israel, including a complete halt to Qassam (rocket) fire and suicide bombings," a senior Hamas official told daily "Haaretz" on Tuesday.
The Hamas official however, warned that if Israel continues to insist with the international boycott and refuses to work with the unity government, the existing partial ceasefire will be in danger, the report said.
Palestinian Authority (PA) Chairman Mahmoud Abbas plans to deliver this offer during his forthcoming meeting with Prime Minister Ehud Olmert, Palestinian sources reportedly said.
The meeting which is tentatively scheduled for Sunday is the third meeting between the two leaders over the last three months.
Israel, meanwhile, is firm on its position saying that if the unity government does not fulfill three international conditions, Jerusalem will boycott the Fatah ministers in the Palestinian government.
Olmert plans to convey the same during the meeting asking Abbas to fulfill Quartet's key conditions of recognising Israel, renouncing violence and honouring previous Israeli-Palestinian agreements.
"This will not be a scolding conversation but a heart-to-heart talk in which Olmert will try to exploit the grace period that remains before the new PA government is established," a government source told the daily.
Palestinians have said that the unity government was unlikely to be finalised until the Olmert-Abbas meeting.
Hamas and Fatah have not yet agreed upon a candidate for the crucial post of interior minister.
Meanwhile, Israel is also working to persuade the European Union, one of the Quartet's four members, along with the United States, Russia and the United Nations, to continue the boycott, until the unity government fulfills the three conditions.
Some countries in the EU have been pushing for resuming talks with moderate elements in the PA but Israeli foreign minister Tsipi Livni, just back from a meeting with EU foreign ministers, said that they still stand firm on quartet's conditions.