Guterres expressed deep concern about the deadly clashes and urged restraint from any action that could lead to additional casualties, particularly measures that could place civilians in harm's way.
Gaza hospitals, running low on blood and overstretched by the huge number of wounded, were reeling after one of the enclave's bloodiest days outside of open war, in which Israeli soldiers shot 773 people with live ammunition, according to the ministry of health.
"The Secretary-General calls for an independent and transparent investigation into these incidents", said a statement by Guterres' deputy spokesman Farhan Haq, which also reaffirmed "the readiness" of the world body to revitalize peace efforts.
His call, on Friday, came as the UN Security Council heard fears of a further escalation in Israeli-Palestinian violence in the Gaza Strip during emergency talks.
"Lethal force should only be used as a last resort with any resulting fatalities properly investigated by the authorities", United Nations deputy political affairs chief Taye-Brook Zerihoun said.
Hamas, the group that has controlled the Gaza Strip since 2007, does not recognise Israel, but a year ago said it was ready to accept an interim Palestinian state limited to Gaza and the West Bank.
"Israel must uphold its responsibilities under worldwide human rights and humanitarian law".
The violence broke out as tens of thousands of Gazans marched near the Israeli border to demand the right of return for Palestinian refugees who fled or were expelled since the creation of Israel.
UN Secretary-General calls for independent investigation into Gaza deaths
Palestinians accused Israel of using disproportionate force, as did Turkey.
In a written statement before the meeting, Israel's ambassador to the United Nations, Danny Danon, blamed Hamas for the violence.
Palestinian President Mahmoud Abbas said the Israeli authorities bore "full responsibility" for Friday's deaths.
Throughout the day, the Office of the UN Special Coordinator for the Middle East Peace Process, known as UNSCO, was in contact with both Palestinian and Israeli security forces and would continue to do so as more demonstrations are expected over the next six weeks.
Hours before the march, a Palestinian farmer was killed when an Israeli artillery shell struck his land in the southern Gaza Strip.
Some Security Council members suggested an investigation and emphasized that Israel should ensure force is only used proportionally.
Israel deployed thousands of troops along the border in anticipation of the mass demonstrations dubbed "Great March of Return" that also sought to pressure Israel to lift its more than decade-long blockade of Gaza.More news: Jesus Christ Superstar has risen ... NBC's ratings!
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