Palestinian medics reported at least 14 people were wounded, including five who were shot.
Israel says it will allow more goods and equipment to enter the besieged Gaza Strip for civilian and international projects following days of heightened tensions.
The announcement came after hundreds of Palestinians demonstrated on Wednesday near the Israeli separation barrier, calling on Israel to ease a crippling blockade days after a similar gathering ended in a deadly crackdown by the Israeli army.
Hamas, which governs Gaza, kept the crowds from approaching the barrier, and the protests ended without a repeat of Saturday’s violence that left one Palestinian dead and an Israeli policeman critically injured.
The defence ministry’s body in charge of Israel’s crossings with the Palestinian territory said in a statement late on Wednesday that it would increase imports of new vehicles, goods and equipment for civilian projects in the Gaza Strip, and issue more permits for Palestinian businessmen from Gaza to enter Israel starting Thursday.
The easing of restrictions would be “conditional upon the continued preservation of the region’s security,” and could be further expanded if the border situation improves, the body known as COGAT said.
Hamas officials said Egypt would also be partially reopening its key border crossing with the Gaza Strip on Thursday.
Egypt has been trying to broker a long-term ceasefire between the two sides since an 11-day Israeli assault on the Gaza Strip in May that killed at least 260 Palestinians, including 67 children, and 13 people in Israel.
Israel and Egypt imposed a devastating blockade on Gaza after Hamas won the election and began governing the territory in 2007.