AMSTERDAM (Reuters) - The prosecutor of the International Criminal Court on Sunday called for an end to violence in the Gaza Strip, adding the Palestinian territories were subject to a preliminary examination by her office and she was monitoring events there closely.

Following the deaths of 29 Palestinians in protest clashes with Israeli forces in the past two weeks, Fatou Bensouda said in a statement "any new alleged crime committed in the context of the situation in Palestine may be subjected to my Office's scrutiny".

The ICC prosecutor opened a preliminary investigation into alleged crimes committed in occupied Palestinian territory, including East Jerusalem, in January 2015, after Palestine was officially admitted as a member of the court.

Israel is not a member of the court but if Israeli citizens commit war crimes or crimes against humanity on the territory of a member state they could fall under the ICC's jurisdiction.

"Violence against civilians - in a situation such as the one prevailing in Gaza – could constitute crimes ... as could the use of civilian presence for the purpose of shielding military activities," Bensouda said.

Bensouda said she would record "any instance of incitement or resort to unlawful force" by either side in the conflict.

A preliminary examination is the earliest phase of a case at the ICC. In it, the prosecutor gathers information and studies whether crimes may have been committed that reach the level of gravity required to open a formal investigation, and whether the court would have jurisdiction.

The ICC only has jurisdiction in cases where a country's government is itself unable or unwilling to prosecute war crimes or crimes against humanity.

(Reporting by Toby Sterling; Editing by Andrew Roche)