CAIRO, April 2 (Reuters) - Egypt's military rulers will meet with Palestinian President Mahmoud Abbas on Thursday to seek ways to ease tension between his Fateh movement and its rival Hamas, Egypt's state news agency said on Saturday.

Reconciling the rival movements running Palestinian affairs is seen as vital to any prospect of Palestinian statehood based on peace with Israel.

Abbas will hold important talks with Field Marshal Mohamed Hussein Tantawi, head of the Supreme Council of the Armed Forces, Egyptian state news agency MENA said.

Fateh took part in US-sponsored direct talks with Israel last year, drawing condemnation from Hamas which seized Gaza from Fateh in 2007 and is hostile to the Jewish state.

Israel tightened a blockade on Gaza after Hamas took control there.

Egypt sponsored six months of talks between Hamas and Fateh in 2009 that led to a draft pact to form a national unity government.

Fateh signed the pact but Hamas refrained, demanding guarantees for international recognition.

Abbas, whose movement still runs affairs in self-ruled areas of the West Bank, said last week he was ready to visit Gaza to end divisions and kick-start a comprehensive dialogue.

Delegations from Fateh and Hamas visited Cairo last week, meeting with officials from Egypt's intelligence agency, the foreign ministry and the Arab League.

The army now runs Egypt after an uprising ousted President Hosni Mubarak on Feb. 11.

(Writing by Marwa Awad; Editing by Michael Roddy)