"Our greatest hope is for peace", he said.
The latest casualties raised the Palestinian death toll to 86 since the protests started six weeks ago.
The march was also directed at the inauguration of the embassy.
In response to the Trump administration moving the embassy, tens of thousands rushed to the land border on the day the embassy is set to open, as guests, including President Donald Trump's daughter Ivanka and son-in-law Jared Kushner, attend the embassy's opening.
The Palestinians, who want their own future state with its capital in East Jerusalem, have been outraged by Trump's shift from previous administrations' preference for keeping the U.S. embassy in Tel Aviv pending progress in peace efforts.
He added that the Palestinians protesting in Gaza were "part of the problem, and not part of the solution". The sides have largely observed a cease-fire since the 2014 war - their third in a decade.
Protests in Gaza have been boiling over for months, with huge numbers of Palestinians joining in what has been dubbed "the Great March of Return". Hamas said four members, including three security men, were among the dead on Monday.
Supreme Eurasian Economic Council to convene in Sochi on 14 May
We highly appreciate Russia's balanced position during Armenia's internal political crisis. Nevertheless, the Kremlin clearly remained skeptical of Pashinyan's intentions.
"What a moving day for the people of Israel and the State of Israel", Netanyahu said. Sirens were constantly wailing as the wounded were carried to nearby ambulances. Groups of young activists repeatedly approached the fence, but were quickly scattered by gunfire and tear gas.
The president also tweeted about the event Monday morning.
Tuesday marks the commemoration of Nakba Day, a term which Palestinians use to describe their forced mass exodus from their homes during the establishment of the State of Israel.
On Monday morning, the United States opened their new US embassy in Jerusalem. Most United Nations members don't recognize Israel's sovereignty over East Jerusalem, arguing instead that the city should possess global status.
The Palestinian Authority in Ramallah on Monday accused Israel of committing a "terrible massacre". "Because when President Trump makes a promise, he keeps it".
Map of Jerusalem showing the changing lines that created the territorial anomaly where the new USA embassy to Israel will be partly located.
Israeli government spokeswoman Michal Maayan said: "We're inviting Ireland to join because the issue of Jerusalem, Jerusalem is the capital of Israel, it's going to be the capital of Israel whatever future settlement we will arrive with Palestinians".
European foreign ministers have said the embassy move is unwise and likely to exacerbate tensions in the region.
Four European countries - Austria, Czech Republic, Romania, and Hungary - have confirmed their participation in the USA move while the European Union opposes the relocation.