The decision to open an investigation was a rare step and comes with Israel having faced international criticism over its use of live fire during unrest along the Gaza frontier.
A rise in cross-border rockets and air strikes in recent weeks has prompted the United Nations and Egypt to try to broker a truce to prevent another all-out conflict.
A Palestinian wounded in May by Israeli fire during deadly clashes on the Gaza border has died of his injuries, the health ministry in the Palestinian enclave said on Tuesday.
A Palestinian armed with an axe was shot dead trying to breach the Gaza-Israel border on Monday, the Israeli army said.
Militants from Hamas, the dominant group in Gaza, and Islamic Jihad fired dozens of rockets and mortar bombs at Israel throughout Tuesday.
Violations of the Geneva Conventions adopted in 1949 following World War II are commonly called "war crimes".
The Turkish foreign ministry has told the consul to leave Turkey "for a period of time", the state-run Anadolu news agency said.
Monday's violence on the border, which took place as the United States opened its new embassy in Jerusalem, was the bloodiest for Palestinians since the 2014 Gaza conflict.
Protests intensified on the 70th anniversary of Israel's founding, as loudspeakers on Gaza mosques urged Palestinians to join a "Great March of Return".