Israel's Prime Minister Benjamin Netanyahu said on Twitter Erdogan was in no position to "preach morality to us" because he supported the Palestinian Islamist movement Hamas which rules Gaza. Haley noted Hamas' track record of antagonizing Israeli security forces and declared in her address that "no country in this chamber would act with more restraint than Israel has".
Earlier, Labour's Emily Thornberry condemned a "horrific massacre".
Mrs May said Israel had a right to defend its borders but the use of live fire and the resulting loss of life was "deeply troubling".
The White House defended Israel on Monday, calling the Gaza protests a "gruesome and unfortunate propaganda attempt" and said responsibility for the deaths "rests squarely with Hamas". "Many of them, shot hundreds of metres from the border, and many of them, children".
Most countries say the status of Jerusalem - a sacred city to Jews, Muslims and Christians - should be determined in a final peace settlement and that moving their embassies now would prejudge any such deal.
On Tuesday, there were no signs that Hamas had made a breakthrough in shaking off the blockade that was imposed by Israel and Egypt in 2007.
The United States opened its new Israel embassy in Jerusalem on Monday.
Tuesday's delayed demonstrations could grow since May 15 is the annual observation of Naqba Day, or Catastrophe Day, which mourns Israel gaining statehood and the displacement of the Palestinians.
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The Palestinians have boycotted the process since Trump's Jerusalem announcement in December.
It also drew the largest crowds as tens of thousands gathered near the border, with the majority not approaching the heavily guarded fence.
The Israeli military said its soldiers had shown restraint and used live ammunition only as a last resort.
An Israeli government spokesman had no immediate reaction to the cascade of criticism. "At a minimum, that would require urging the Israelis to stop using lethal force against unarmed protesters". Others continued to protest armed with rocks and burning tires as Israel reportedly killed at least two more demonstrators during the "March for Return" Tuesday. Talks aimed a finding a two-state solution to the conflict have been frozen since 2014.
Rep. Steve Russell, another Oklahoma City Republican, called the embassy move a historic and long overdue recognition of reality.
Was the violence linked to the opening of the embassy?
Crowds in Gaza swelled to an estimated 30,000 by 2:30 p.m., 90 minutes before the new United States embassy was slated to officially open in the Arnona neighborhood of Jerusalem.
The move by the United States would only further strengthen the resolution and determination of the oppressed Palestinians in confronting and resisting occupation, it said.
Jared Kushner and Ivanka Trump were among the guests headlining the Jerusalem embassy opening, a move condemned by Palestinians and widely criticized by world leaders who consider the relocation a provocation.
The confluence of events led to split-screen coverage of Monday's embassy unveiling, with USA guests led by President Trump's daughter and son-in-law, Ivanka Trump and Jared Kushner, smiling and celebrating inside the embassy as, along the Gaza border, black smoke billowed from burning tires and gunshots rang out in what an IDF spokesperson called a day of "unprecedented violence".
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