By Nidal al-Mughrabi

GAZA, March 23 (Reuters) - Tens of thousands of Palestinians rallied in Gaza on Sunday to show support for their Islamist Hamas government, which has long been at loggerheads with Israel but is now shunned by Egypt as well.

The military-backed government that toppled the Muslim Brotherhood, Hamas's ideological kin, in Cairo last year has blacklisted the Brotherhood and Hamas as terrorist groups and clamped down on people, goods and arms crossing the Sinai-Gaza border.

Hamas tried in vain to mollify Egypt by insisting that its hostility was directed exclusively at Israel, but is now turning up the rhetoric.

"The punishment of the people of Gaza must end," Ismail Haniyeh, head of the Hamas government, told the rally in a speech interspersed with chants of "Jihad is not Terrorism" over the loudspeakers.

"Why punish Gaza? Was it because it achieved victory against the Occupier? Why punish Gaza? Was it because it took up the rifle against Israel?" Haniyeh said.

"We are living through a difficult stage and harsh challenges, but we are not terrified and we are not defeated. We have become familiar with difficulties and this stage is not the most difficult."

Hamas has repeatedly fought Israel, which withdrew from the Gaza Strip in 2005. The Islamists won a Palestinian legislative election the next year and, after a uneasy power-share with the U.S.-backed rival faction Fatah, seized control of Gaza in 2007.

OPPOSITION TO PEACE TALKS

Sunday's rally was intended to commemorate three top Hamas leaders, including the group's founder, Sheikh Ahmed Yassin, who was assassinated by Israel a decade ago.

The tone of defiance appeared aimed in part at undermining Palestinian President Mahmoud Abbas of Fatah, who holds sway in the Israeli-occupied West Bank and is holding peace talks with Israel under Washington's auspices.

"We call upon the Palestinian negotiator to quit this pointless track and not to extend negotiation," said Haniyeh.

Though Hamas has largely held fire since its last war with Israel, in November 2012, the Israelis have been uncovering tunnels dug from Gaza to allow cross-border attacks in the next confrontation. Haniyeh said the tunnels showed his faction's dedication to fighting Israel until its eventual destruction.

"From below ground and above ground, you, the Occupiers, will be dismissed. You have no place in the land of Palestine."

Haniyeh described Egypt as "brother, friend and neighbour", but another Hamas official based in the West Bank, Hassan Youssef, had harsher words.

"We say to the authors of the coup in Egypt, the criminals who support the Occupation (Israel), that the blockade will not work," he said in a televised speech.

Cairo's cold shoulder has exacerbated Hamas's isolation since it quit its headquarters in Damascus in protest at Syrian President Bashar al-Assad's crackdown on opposition groups, a move that led Iran to cut off funding.

Palestinian officials said Hamas was now in fence-mending talks with Tehran, though their outcome remained unclear. (Writing by Dan Williams; Editing by Kevin Liffey)