As Antonio Guterres made the call that had been preceded by a UN Security Council meeting, Israel warned that it would have to expand its response if clashes continue.
UN Secretary-General Antonio Guterres on Friday called for an "independent and transparent investigation" after 16 Palestinians were killed and hundreds more wounded during clashes with the Israeli military, a spokesman said.
His call came as the UN Security Council heard concerns of a further escalation in Israeli-Palestinian violence in the Gaza Strip during emergency talks.
"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 revitalise peace efforts.
But as the call was made in New York, Israel warned that it will target "terror organizations" in Gaza if violence along the territory's border with Israel drags on.
The protests on Friday by thousands of Palestinians had left at 16 dead and 1,400 injured, the Palestinian Health Ministry said.
It was a figure that according to Brig. Gen. Ronen Manelis, the chief army spokesman, had been exaggerated. He claimed that that several dozen at most were injured by live fire while the rest were merely shaken up by tear gas and other riot dispersal means.
Manelis said that Israel "will not allow a massive breach of the fence into Israeli territory."
He said that Hamas and other Gaza militant groups are using protests as a cover for staging attacks. If violence continues, "we will not be able to continue limiting our activity to the fence area and will act against these terror organisations in other places too," he said.
Gaza City's Shifa Hospital received 284 injured people Friday, the majority with bullet injuries, spokesman Ayman Sahbani told The Associated Press. He said 70 were under the age of 18 and 11 were women.
He said 40 surgeries were performed Friday and that 50 were planned Saturday. "These are all from live bullets that broke limbs or caused deep, open wounds with damage to nerves and veins," he said.
Among those recovering from surgery was 16-year-old Marwan Yassin who had thrown stones with a slingshot at the fence Friday and was shot in both legs. One of his legs was wrapped in bandages and the other had a cast and metal fixtures.
His mother said at his bedside that she would ban him from future protests.
On Saturday there were no immediate reports of clashes, but funerals were underway for those who had died in the clashes.
Guterres spokesman also said that the UN chief "also appeals to those concerned to refrain from any act that could lead to further casualties and in particular any measures that could place civilians in harm's way."
Kuwait requested the emergency meeting that discussed the unravelling situation in Gaza, which saw the conflict's deadliest single day since the 2014 Gaza war.
Palestinian UN envoy Riyad Mansour accused Israel's "well armed" forces of excessive use of force on a peaceful demonstration while Israel accused protesters of throwing stones and rolling burning tyres in an attempt to breach the border.
Britain and the United States expressed regret that the timing of the meeting -- the first night of Passover -- meant Israeli officials could not attend. Leading ambassadors sent deputies in their place.
"It's vital that this Council be balanced in its approach," a US diplomat told the meeting. "We should have found an arrangement for all parties to participate tonight," he added.
"We are deeply saddened by the loss of life today," the diplomat added. "Bad actors who use protests as a cover to incite violence endanger innocent lives."
"The risk of escalation is very real," the French representative said. "There is the possibility of a new conflict in the Gaza Strip."
In a written statement before the meeting, Israel's ambassador to the United Nations, Danny Danon, blamed Hamas for the violence.
"While Jews around the world gathered with their family at the Seder table to celebrate the Passover holiday, the Palestinians sunk to a new deceitful low so that they could use the UN to spread lies about Israel," Danon later said.
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.
Israeli troops used tear gas and live fire to force back Palestinians who approached the heavily fortified border fence.
Israeli tank fire and an air strike also targeted three Hamas sites in the Gaza Strip after what the military said was an attempted shooting attack against soldiers along the border that caused no injuries.
Annual "Land Day" protest
The Palestinian protest marked "Land Day," an annual commemoration of the deaths of six Arab citizens of Israel killed by Israeli security forces during demonstrations over government land confiscations in northern Israel in 1976.
The demonstrators demanded that Palestinian refugees be allowed the right of return to towns and villages which their families fled from, or were driven out of, when the state of Israel was created in 1948.
They gathered at multiple sites throughout the blockaded territory, which is flanked by Israel along its eastern and northern borders.
Smaller numbers approached within a few hundreds metres of the heavily fortified border fence, with Israeli troops using tear gas and live fire to force them back.
Turkey condemns Israel
Turkish foreign ministry expressed outrage over the killings in Gaza, in a statement on Friday.
"We condemn Israel for using disproportionate forces on peaceful Palestinian demonstrators. We are concerned for the people who lost their lives and injured in Israeli security forces intervention," the statement said.
"Israel must stop activities that increase tension in the region as soon as possible. We invite international communities to put their utmost effort to dissuade Israel from such aggression."
Hamas hails turnout
Hamas spokesman Fawzi Barhoum on Friday praised the turnout.
"The large crowds ... reflect the Palestinian people's determination to achieve the right of return and break the siege and no force can stop this right," he said.
Earlier in the day, before the main protests began, a Palestinian farmer was killed by Israeli tank fire near the border, the health ministry said.
The Israeli military said the tank fire came after "two suspects approached the security fence ... and began operating suspiciously."
Witnesses said the military had used a drone in at least one location to drop tear gas.