(Updates with Ismail Haniyeh's remarks)

LONDON, May 2 (Reuters) - Major powers called for a shift in strategy toward the Hamas-controlled Gaza Strip on Friday, backing Egyptian efforts to broker an informal truce between Israel and Palestinian militants and to ease a crippling embargo of the coastal territory.

The stance by the Quartet of Middle East peace mediators increases pressure on Israel to ease its blockade, tightened last June after Hamas Islamists seized control of the Gaza Strip from Palestinian President Mahmoud Abbas' more secular Fatah movement.

"Principals strongly encouraged Israel, the Palestinian Authority, and Egypt to work together to formulate a new approach on Gaza that would provide security to all Gazans, end all acts of terror (and) provide for the controlled and sustained opening of the Gaza crossings for humanitarian reasons and commercial flows," the European Union, Russia, the United Nations and the United States, said in a statement.

Ismail Haniyeh, head of the Hamas government in Gaza, said Egypt has concluded the formulation of a united Palestinian position which will be submitted to Israel.

"If the Israelis reject this position, then first, we will not surrender, and second, we will not expect that Egypt, the author of the proposal and the sponsor of this position, will accept the continuation of the siege and the continuation of the closure of Rafah crossing.

"We would not accept new (Israeli) conditions ... The ball is now in the Israeli court and if they decide on rejection, I think that neither we as a people nor Egypt will accept the closure of the crossings or the continuation of the siege."

The Quartet had previously urged Israel to consider handing over control of the border crossings to Abbas's government and security forces but had not taken a unified stand on the Egyptian efforts.

On Monday, a senior Israeli official said the Jewish state would likely agree to an informal Egyptian-sponsored truce with Palestinian militants in Gaza if cross-border rocket attacks on Israel and arms smuggling into the territory ended.

The split between Hamas, which remains officially committed to the destruction of Israel, and Fatah, which is engaged in peace talks with Israel, is a major obstacle to U.S. President George W. Bush's hope to secure a statehood deal by the end of 2008.

(Reporting by Arshad Mohammed and Nidal al-Mughrabi; Editing by Samia Nakhoul)