Israel's foreign minister arrived in Egypt's capital Cairo on Sunday in a bid to shore up a cease-fire between Israel and the Palestinian militant group, Hamas.
Israel - backed at times by the United States - accuses the council of anti-Israel bias and has generally refused to cooperate with its investigators.
In an apparent allusion to tactics of Hamas, she said it was a violation of worldwide humanitarian law to locate military assess in densely populated civilian areas, or to launch attacks from them.
Israeli Prime Minister Benjamin Netanyahu met Egyptian intelligence chief Abbas Kamel in Jerusalem to discuss "strengthening cooperation" between their countries, Netanyahu's office said.
Motegi had telephone talks with the foreign ministers of both sides earlier this week, offering assistance to Gaza and also requesting them to continue a ceasefire.
Hamas leader Ismail Haniyeh is expected to visit Cairo this week, according to the group's spokesman Abdelatif al-Qanou, who also said Hamas is open to discussing a prisoner swap with Israel.
Rocket and other fire from Gaza claimed 12 lives in Israel, including one child and a Palestinian teenager, an Israeli soldier, one Indian national and two Thai workers, medics say. Bachelet said Hamas' indiscriminate rocket fire during the conflict was also a clear violation of the rules of war.
Egypt played a pivotal role in negotiating the May 21 ceasefire between Israel and Hamas that brought an end to 11 days of deadly fighting.
Israeli strikes on Gaza killed 248 Palestinians, including 66 children, and have wounded more than 1,900 people, the Gaza health ministry says.
Hamas has pledged not to touch "a single cent" of global aid to rebuild Gaza.
Netanyahu said the meeting in Jerusalem dealt with regional security issues and ways to prevent Hamas from siphoning off civilian aid to strengthen its capabilities.
Sisi also tasked Kamel with working to help iron out political divisions between Hamas in Gaza and Fatah in the Israeli-occupied West Bank, the Egyptian officials said.
The UN High Commissioner for human rights spoke to the Human Rights Council, chronicling the "most significant escalation of hostilities since 2014" that left devastation and death in the Gaza Strip before a cease-fire last week.
There is controversy about how many of those killed in Gaza were combatants, and how many were civilians.
And while the council has previously ordered eight investigations into rights violations committed in the Palestinian territories, this would be the first one with a mandate to examine "root causes" in the drawn-out conflict, and also to probe systematic abuses committed within Israel.
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