Gaza militants have fired rockets at Israel, defying the Israeli military's warning that it will not tolerate renewed attacks on the country's south.
In the West Bank, authorities discovered the body of a second Palestinian protester killed in clashes a day earlier.
The events are likely to further raise tensions in the region, already heightened this week by the death of a Palestinian prisoner from cancer in an Israeli jail and renewed cross-border fighting.
Several rockets were fired from Gaza early on Thursday but only one exploded in Israel, causing no injuries, the military said. It said the other projectiles exploded prematurely inside Gaza.
The militants from the coastal territory have fired several rockets at Israel since November, when an informal truce took hold after eight days of fighting triggered by almost daily Palestinian rocket attacks. Israel retaliated for the first time this week and Moshe Yaalon, the new defence minister, warned that he will not allow rocket attacks to become routine again.
Israel holds Gaza's Islamic militant Hamas rulers responsible for all attacks from there. A small al Qaida-influenced group has been suspected in some of the more recent attacks.
Earlier, the body of a Palestinian man was found near a military post in the West Bank, reported the official Palestinian news agency Wafa.
Protests in the territory had turned violent late on Wednesday when Palestinians threw firebombs at soldiers who shot and killed one protester. Mohammed Ayyad, a spokesman for the Palestinian Red Crescent, said both Palestinians were shot in the chest.
The Israeli military said soldiers opened fire at Palestinians who attacked them with firebombs and that it was investigating the incident.
Demonstrations first erupted across the West Bank on Tuesday over the death of a Palestinian prisoner who died from cancer. The prisoner, 64-year-old Maysara Abu Hamdiyeh, was serving a life sentence for a 2002 foiled bombing of a busy Jerusalem cafe.