A Turkish government minister and spokesman, Bekir Bozdag, also accused Israel's most powerful ally, the United States, of helping fuel Palestinian outrage by moving the U.S. Embassy from Tel Aviv to Jerusalem.
Palestinian leaders have called Monday's events a massacre and the Israeli tactic of using live fire against the protesters has drawn worldwide concern and condemnation.
The cycle of violence in Gaza needs to end, said Mladenov.
Speaking alongside May, Erdogan warned that history would not forgive Israel or the United States for moving the American embassy to Jerusalem in defiance of outrage in the Islamic world.
The Gaza protests were part of "The Great March of Return" ― weeks of demonstrations running from late March until the annual Nakba Day on May 15, which commemorates the displacement of Palestinians when the state of Israel was created in 1948.
The Gaza health ministry, which provided the toll from Monday's violence, said a nine-month-old girl died from tear gas exposure, but medical officials later cast doubt on that claim, saying the infant had a pre-existing medical condition.
Rights groups have said the use of potentially lethal force against protesters who pose no immediate threat to soldiers' lives is unlawful.More news: I won't hinder Rooney if he wants to leave Everton, insists Allardyce
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But not until they accept that the Israel they loathe is in the neighborhood to stay.
After President Trump's announcement past year, the Czech Republic has said that Jerusalem is the "capital of the State of Israel, in its 1967 borders".
Speaking alongside the British prime minister, Mr Erdogan said: 'While we are focusing our talks on the Syria issue, yesterday unfortunately significant incidents have unfolded in Palestine after the United States made a decision to move their embassy to Jerusalem from Tel Aviv.
Following Monday's border clashes Turkey pulled its ambassadors to Israel and the US and expelled the Israeli ambassador in Ankara.
As to whether he knows of any efforts to calm the situation by the Egyptians or any other player in the region, Amidror said that Egypt has the ability to speak with both sides.
Hundreds took to the streets in Tel Aviv, Israel, and other cities worldwide this week to protest the Israeli military killing dozens of Palestinians demonstrating on the Gaza border. We will see this reality.
Hundreds of protesters carrying Palestinian flags and wearing keffiyehs took to the streets of the Loop Tuesday evening, one day after Israeli soldiers shot and killed at least 59 Palestinians during mass protests along the Gaza border as the US embassy in Israel moved from Tel Aviv to Jerusalem.