Riyad Mansour made the complaint that Israel broke a 2-day-old cease-fire that followed eight days of shooting and shelling between the two sides, the Palestinian Ma'an news agency reported.
A 20-year-old man was killed and 19 others were wounded in Friday's incident, Mansour said.
At least 170 Palestinians and six Israelis were killed in the eight-day conflict, the report said.
Palestinian Authority President and Fatah leader Mahmoud Abbas has kept his distance from the issue in Gaza, which is run by the rival Hamas party, the BBC said.
Instead, he has asked for a vote of the U.N. General Assembly to grant Palestinians observer status that would that open doors to international court proceedings against Israel, the report said.
Observers told the BBC said it appears Abbas has the necessary two-thirds majority at the United Nations to gain non-voting status.