QUSRA, West Bank, Sept 5 (Reuters) - Jewish settlers set fire to a mosque in the occupied West Bank on Monday, Palestinians said, in a likely reprisal for Israel's dismantling of three buildings in an unauthorised settlement outpost hours earlier.

Abdel Azeem Wadi, a member of the village council in Qusra near the Palestinian city of Nablus, said settlers threw burning tyres into the mosque, damaging the entire first floor.

Palestinian Prime Minister Salam Fayyad denounced the attack as an act of terrorism.

"These acts are what threaten to pull the region into a cycle of violence," Fayyad's office said in a statement, adding that the Palestinians themselves would not revert to violence.

An Israeli police spokesman said police and army personnel had entered the village to inspect the damage to the mosque and that the investigation was ongoing.

Earlier on Monday, Israeli authorities enacted a court order and demolished three houses in Migron, a Jewish hilltop outpost.

The names of Migron and a second outpost were written in Hebrew on the mosque walls.

Some settlers have threatened to exact a price on Palestinians in response to Israeli government actions against unauthorised settlements.

Last month, the Supreme Court ruled that Israel must evacuate the entire Migron outpost by the end of March 2012, a spokeswoman for the court said.

Six people who scuffled with police during the demolition were arrested, police said.

Migron is one of about 100 small outposts that settlers built without government approval on land that Israel captured in a 1967 war and which Palestinians want for a future state.

The World Court deems all Israeli settlements illegal under international law -- a ruling that Israel rejects.

Settler-related incidents resulting in Palestinian injuries and damage to property are up more than 50 percent this year, according to the U.N. Office for the Coordination of Humanitarian Affairs, which documents violence in the Palestinian territories.

Palestinian authorities say settlers have attacked at least six mosques in the West Bank in the past two years. Fayyad's office criticised the Israeli police for failing to track down those behind previous such violence.

"The prime minister holds Israel completely responsible for the continuation of these terrorist acts because of its failure to pursue the perpetrators of this type of attack on previous occasions and bring them to account," its statement said.

Settler and military officials said last week that Israel's military has been training Jewish settler security units to cope with any eruption of Palestinian protests alongside a planned bid for statehood at the United Nations this month. (Reporting by Abed Omar Qusini, Tom Perry and Ari Rabinovitch; Editing by Louise Ireland)