By Nidal al-Mughrabi

GAZA, Oct 19 (Reuters) - Hamas, its Gaza Strip stronghold cut off by the new military-backed government in Egypt, called upon rival Palestinian President Mahmoud Abbas on Saturday to end their six-year schism and form a unity government.

Abbas's secular, U.S.-backed Fatah faction lost a 2006 ballot to Islamist Hamas. They sat in an uneasy alliance until a civil war the following year left Hamas ruling Gaza while Abbas's authority was limited to the Israeli-occupied West Bank.

Egypt brokered a Palestinian reconciliation deal in 2011 but it was never implemented. In Cairo, meanwhile, Islamist President Mohamed Mursi was toppled by the army, which treats Egypt's Hamas neighbours as security threats.

"Our conditions do not allow for keeping up differences," Ismail Haniyeh, prime minister in the Gaza administration, said in a speech calling on Abbas and Fatah to renew dialogue with Hamas, schedule new elections and enter a temporary power-share.

"Let's have one government, one parliament and one president," Haniyeh said.

The overture was received coolly by Fatah, whose leader, Abbas, is engaged in a new round of U.S.-sponsored peace talks with Israel. Hamas refuses coexistence with the Jewish state.

Ahmed Assaf, a Fatah spokesman, said Haniyeh's speech "included nothing new, neither a clear plan nor a certain timetable".

Pressured by the deterioration of ties with former regional backers Syria, Hezbollah, Iran, as well as by Mursi's fall and the ensuing Egyptian crackdown on Palestinian tunnels used to smuggle arms and commercial goods into Gaza, Hamas is in steep financial decline.

Haniyeh sought to soften tensions with Cairo, denying Egyptian accusations the group had intervened in the internal unrest on behalf of Mursi's Islamist supporters.

Hamas has also tried to fend off allegations that it was aiding Islamist militants in the lawless Egyptian Sinai desert, which borders both Gaza and Israel.

"We have not intervened in internal Egyptian affairs, neither in Sinai nor anywhere else in Egypt," Haniyeh said.

Cairo's closure of some 1,200 smuggling tunnels on the Egypt-Gaza border has deepened Palestinian material shortages, adding to pressure from a long-standing Israeli embargo on the coastal strip, and denied Hamas a major source of tax revenue.

Haniyeh said Palestinians could do without the smuggling tunnels were Egypt to open up its border with Gaza rather than support the Israeli blockade.

But he hinted that Hamas was hard at work digging a different kind of tunnel - under the border with Israel, to strike at the Jewish state in a future conflict. Israel and Hamas fought an eight-day war in November.

The Israelis unearthed one such tunnel last week, saying its Palestinian operators apparently planned to kidnap a soldier or set off underground explosives.

Hamas did not claim or deny responsibility for that tunnel. But Haniyeh said in the speech that "thousands of heroes have been working in silence, below ground, to prepare for the coming battles in Palestine". (Additional reporting by Ali Sawafta in Ramallah; Editing by Dan Williams and Mike Collett-White)