GAZA, June 24 (Nidal al-Mughrabi/Reuters) - The Gaza Strip's governing Hamas on Sunday welcomed the victory of the Muslim Brotherhood in Egypt's presidential vote, saying its ideological ally's success would help the Palestinian cause.

The impoverished enclave burst into celebration upon hearing that the Muslim Brotherhood's Mohamed Morsy had won elections held after former president Hosni Mubarak fell to a people's revolt last year.

Locked in a long power-struggle with its secular Palestinian rivals, Hamas had a mixed relationship with the previous, U.S.-aligned Egyptian president, who supported Israel's blockade on Gaza.

We will look to Egypt to play a big, leading role, a historic role, regarding the Palestinian cause, in helping the Palestinian nation get freedom, return home, and totally end the Gaza siege, Ismail Haniyeh, head of the Hamas government, told Reuters Television.

In Gazan streets, the jubilation recalled that which greeted Hamas's shock victory in a Palestinian election in 2006.

Sweets were handed out to passersby, many of them waving Egyptian flags. Thanksgiving sermons echoed from mosque loudspeakers and gunmen fired in the air - the latter accidentally killing a man and wounding three other people, medical officials said.

Hamas and the Muslim Brotherhood share ideological roots, including a hostility to Israel, with which Egypt signed landmark peace accords in 1978-1979.

The U.S.-backed Palestinian President Mahmoud Abbas, who has pursued stop-start peace negotiations with Israel, also had warm words for the Muslim Brotherhood, calling Morsy the choice of the great people of Egypt.

Saeb Erekat, a senior Abbas aide, said the democratic vote for Morsy meant the Palestinian cause was the Number One priority for all Egyptians.

But Erekat said Palestinians had to heal the five-year-old and sometimes bloody schism between Hamas and Abbas's once-dominant Fatah faction.

Regardless of who the Egyptian president is, Palestinian reconciliation is a Palestinian matter, and if we do not help ourselves, no one will, Erekat said. (Additional reporting by Ali Sawafta in Ramallah; Writing by Dan Williams; Editing by Andrew Osborn)