FACTBOX: Challenges facing Hamas Islamists ruling Gaza Strip

(Reuters) - An Israeli border blockade of the Gaza Strip has underscored the tough challenges ahead for Hamas Islamists who violently wrested control of the Gaza Strip from Palestinian President Mahmoud Abbas's Fatah faction in June.

Following are some of the problems Hamas is likely to face in the coming year:

* Israeli Prime Minister Ehud Olmert and Abbas have pledged to try to seal a peace treaty before U.S. President George W. Bush leaves office in January 2009. An agreement heralding the creation of an independent state could boost support for Abbas among Palestinians, at Hamas's expense, and spur him to call an early election. Polls have shown that Hamas has lost popularity since its violent takeover of Gaza and enforcement of its rule in the territory.

* Olmert has pledged to "wage war" against Hamas if rocket attacks on southern Israel, condemned by Abbas, continue from the Gaza Strip. Such a campaign could target Hamas leaders in the territory or escalate into a widescale ground invasion.

Palestinian analysts say Hamas is using the rocket attacks, which are also carried out by other militant groups, both to counter Israeli military strikes and also as a bargaining chip, to force Israel into a truce and an easing of Gaza border closures, which this week included a cutoff of fuel supplies.

Hamas also continues to hold an Israeli soldier, Gilad Shalit, seized by militants who tunneled into Israel from the Gaza Strip in 2006.

* Tensions with Fatah remain high and Hamas says at least 1,500 of its members have been jailed by Abbas's security services in the occupied West Bank. Fatah says Hamas has been arresting and mistreating its activists in the Gaza Strip. Abbas has said a dialogue with Hamas cannot resume until the group reverses what he describes as its "coup" in the Gaza Strip, territory it wrested from Fatah in June. Hamas rejects Abbas's conditions.

* Hamas continues to be shunned by factions within the Palestine Liberation Organization, as well as by many Arab countries and the West. The group has spurned international demands to recognize Israel, renounce violence and accept existing Israeli-Palestinian interim peace agreements. Hamas leaders have offered a long-term truce with Israel in return for a viable Palestinian state in the occupied West Bank and Gaza Strip.

(Writing by Nidal al-Mughrabi and Wafa Amr; Editing by Charles Dick)