By Asma Alsharif and Dan Williams

CAIRO/JERUSALEM (Reuters) - Hamas rejected on Saturday as insufficient offers made in Cairo to Palestinian negotiators seeking to end Israel's offensive in the Gaza Strip, and raised the possibility of renewed fighting when the current truce expires.

Israel said it had also not yet accepted any proposals made in the Egyptian-mediated talks but, like the Palestinians, its envoys would continue attending them on Sunday.

The ceasefire concludes on Monday night.

Hamas, Gaza's dominant Islamist group, wants an Israeli-Egyptian blockade on the coastal enclave lifted, as well as the establishment of a seaport and airport, as part of any enduring cessation of hostilities with the Jewish state.

"Israel must accept the demands of the Palestinian people or face a long war," Osama Hamdan, the head of Hamas's foreign affairs, said on Facebook.

Israel, which launched its offensive on July 8 after a surge in cross-border Hamas rocket attacks, has shown scant interest in making sweeping concessions. The Israelis want Gaza to be disarmed under any long-term deal - something Hamas rules out.

Egypt, which is mediating between the sides and, like Israel, views Hamas as a security threat, has given little detail on any progress in the talks.

"As of now, Israel has not agreed to any proposals," an Israeli official said on condition of anonymity.

"Understandings (on a long-term truce) will be reached only if they clearly satisfy Israel's security interests," the official added, without elaborating.

Israeli envoys were due to return to Cairo on Sunday, as was a Palestinian delegation including representatives of Hamas and of U.S.-backed President Mahmoud Abbas, who brought his former Islamist rivals into a unity government in April.

Speaking in Ramallah, the seat of his government in the Israeli-occupied West Bank, Abbas promoted Cairo's mediation. Turkey and Qatar, regional powers sympathetic to Hamas, have also sought to serve as go-betweens - to Israel's chagrin.

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"Our goal is to stop the fighting and to stick to the Egyptian initiative, and no other," Abbas said in a televised speech.

INDIRECT NEGOTIATIONS

The United Nations said 425,000 of the 1.8 million population of Gaza have been displaced by the war, which has killed more than 1,900 Palestinians and, on the Israeli side, 64 soldiers and three civilians.

Most of the Palestinian dead have been non-combatants, Gaza hospital officials say.

Israel and the Palestinians agreed on Wednesday to extend a ceasefire agreement in Gaza by five days to continue indirect negotiations on a lasting truce.

The two sides are not meeting face-to-face in Cairo: Israel regards Hamas, which advocates its destruction, as a terrorist group.

The Gaza offensive has had broad public support in Israel. However, the prospect of a long-term truce that improves Hamas's economic or diplomatic standing has drawn misgivings among Israelis and within Prime Minister Benjamin Netanyahu's rightist government.

Some Israeli opposition figures point to the war, and the intractable relationship with Hamas, as cause to rekindle peace talks with Abbas that Netanyahu froze over the Palestinian leader's pact with Hamas.

Abbas, for his part, had chafed at Jewish settlement-building in the West Bank, where, along with Gaza, Palestinians seek statehood.

Several thousand Israelis from left-wing parties and activist groups demonstrated against government policy in Tel Aviv on Saturday.

"When there is no peace, war comes," read one protestor's sign.

(Additional reporting by Ali Abdelatty in Cairo, Nidal al-Mughrabi in Gaza and Mustafa Abu Ganeyeh in Jerusalem; Editing by Erica Billingham, Stephen Powell and Sophie Hares)