JERUSALEM—The Israeli military detained a senior official of the Islamist group Hamas and accused him of inciting attacks, a step to try to stem the latest wave of violence amid new clashes Tuesday.

Palestinians mounted four more attacks on Israeli citizens and security forces and Palestinian media reported that clashes broke out on the border of the Gaza Strip, the densely populated, impoverished territory ruled by Hamas. One Israeli and five Palestinians—four of them assailants—were killed.

United...