FACTBOX: Challenges facing Palestinian leader Abbas

RAMALLAH, West Bank (Reuters) - Palestinian President Mahmoud Abbas is engaged in peace talks with Israel, a move opposed by Hamas Islamists running the Gaza Strip and complicated by an Israeli closure of the territory's borders.

Following are some of the challenges he faces:

* Restoring control over the Hamas-run Gaza Strip.

The loss of the impoverished coastal territory weakens Fatah leader Abbas's negotiating position with Israel and jeopardizes his goal of establishing a Palestinian state in the Gaza Strip and in the occupied West Bank.

Abbas has conditioned renewed dialogue with Hamas on it relinquishing its hold on the Gaza Strip and accepting early presidential and parliamentary elections. Hamas has rejected those terms.

* Meeting a goal of a peace agreement with Israel by the end of the year.

Even as Israeli and Palestinian negotiating teams resume talks on the conflict's most contentious issues after seven years of violence, Abbas and Israeli Prime Minister Ehud Olmert are already at odds over the structure of a peace document they hope to finalize before U.S. President George W. Bush leaves office in January 2009.

Abbas seeks a full peace treaty and wants to declare a Palestinian state this year. Olmert wants a general "framework" agreement that would not end with a statehood declaration but outline how core issues, such as borders and the future of Jewish settlements, Jerusalem and Palestinian refugees, would be resolved.

* Keeping peace hopes alive while Israel and Hamas do battle.

Abbas has repeatedly called for an end to rocket attacks against Israel by militants in the Gaza Strip. But Israel's military response, such as its killing of 35 Palestinians -- most of them militants -- in raids and air strikes in the territory last week have angered the Palestinian public and pushed him into a corner.

Palestinian officials also have condemned Israeli raids to arrest militants in the West Bank, saying the operations undermine Abbas's attempts to restore law and order in the area and weaken Hamas's influence in the territory.

(Writing by Jeffrey Heller and Wafa Amr, Editing by Richard Balmforth)