* Settler violence against Palestinians a problem
* Hamas rockets, Israeli air strikes also condemned
By Robert Evans
GENEVA, March 24 (Reuters) - The building of Israeli settlements and attacks by settlers on Palestinians are a major source of much abuse of rights in the occupied territories, the United Nations' top human rights official said on Monday.
Human Rights High Commissioner Navi Pillay also expressed concern at a recent surge in violence in and around the Gaza Strip by both local groups and Israeli forces.
"Israeli settlement-related activities and settler violence are at the core of many of the violations of human rights in the West Bank, including East Jerusalem," she told the U.N.'s 47-nation Human Rights Council in Geneva.
The settlements not only had a significant impact on the right to Palestinian self-determination, but activities around them "also violate the entire spectrum of Palestinians' social, cultural, civil and political rights," she said.
"Despite repeated calls for Israel to cease settlement activity, ongoing settlement construction and acts of settler violence continue with devastating consequences for Palestinian civilians," said Pillay, a former judge of the International Criminal Court who has visited Israel and the territories.
Most countries deem Israel's settlements in the West Bank illegal and an obstacle to peacemaking. Palestinians decry them as a barrier to achieving a viable state, while Israel considers some of its settlements as a security buffer.
Settlers view the West Bank as a biblical birthright.
Israel withdrew its troops and settlers from Gaza in 2005, and Hamas - an Islamist group which rejects Israel's existence - seized control of the territory two years later, fueling tension which often leads to cross-border violence.
The Gaza violence, Pillay declared, was reflected in increased rocket fire by Palestinian armed groups directed at Israel and Israeli airstrikes on the area.
She said "the targeting of civilians and the indiscriminate firing of rockets towards Israel is a violation of international law. The response through air strikes by Israel is excessive and often causes destruction to personal and public property."
Pillay said an Israeli blockade of Gaza must be lifted, "with due regard to Israeli security concerns." Egypt also blockades Gaza from its side of the border.
Referring to the West Bank administered by the Palestinian Authority, she said U.N. monitors there had documented "a dramatic increase in fatalities and injuries in incidents of use of force by Israeli security forces" in 2013.
There was an urgent need to ensure accountability for such incidents through independent investigations into allegations of unlawful killings or torture and ill-treatment and to prosecute those responsible, Pillay said.
Israel's foreign ministry has been on strike since Sunday. Other officials had no immediate response to Pillay's remarks.
(Reporting by Robert Evans; Editing by Tom Heneghan)