He added: "As the years go on and the occupation entrenches itself we are here to stand shoulder to shoulder with the Palestinians until Palestine is free".
This was the ninth Gaza tunnel destroyed by Israel since October 30, five of which crossed the border into Israeli territory, the rest inside the coastal enclave.
There are growing concerns that if Israel and Hamas dig in, a widespread border breach could lead to large numbers of casualties.
Gaza's Health Ministry reported Saturday evening that a 15-year-old Palestinian died of wounds he sustained during Friday's protests along the border. Forty protesters were killed and more than 1,700 wounded by Israeli troops since late March. Ten of the injured on Friday were in serious condition, among them a 16-year-old with a shot to the head. Rights group say the use of potentially lethal force against unarmed protesters is unlawful.
The protests are part of a campaign to break the blockade imposed by Israel and Egypt after the Islamic militant Hamas overran Gaza in 2007.
The embassy's inauguration comes five months after President Donald Trump recognized Jerusalem as Israel's capital, a move that outraged Palestinians as blatantly pro-Israel.
Clashes were also reported in the West Bank.
The official ceremony for the relocation of the US embassy in Jerusalem will be held on Monday, May 14 in the Jerusalem district of Arnona, and coincides with the 70th anniversary of the Palestinian people's Nakba, or "catastrophe", which marks the creation of Israel in which 700,000 Palestinians were expelled from their land.
Ultimately, some 700,000 Palestinians fled their homes - or were forcibly expelled by invading Jewish forces - while hundreds of Palestinian villages and cities were razed to the ground. Cooking gas and fuel, which are delivered to Gaza through Kerem Shalom on a daily basis, are the first and most essential items likely to be affected.
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The incursion took place during a weekly mass protest in which thousands of Palestinians gathered along the Israel-Gaza frontier.
Media reported that France and other European Union members presented a statement that includes three main clauses: the European Union considers East Jerusalem as a capital of two states, the city's final status is decided through negotiations, and no European Union country would move its embassy to Jerusalem as the USA would do.
In an area east of Gaza City, protesters burned tires, releasing large plumes of black smoke, and threw stones.
Specialized IDF drones created to destroy the burning kites midair were used successfully for the first time during Friday's protests, Walla news reported. One of the kites was downed by a small Israeli drone. "We want peace, we want to end this violence and have our independent state and live side by side democratically with Israel and our Arab neighbors", said the Ambassador Hassassian.
Though they were initially planned as non-violent demonstrations, the protests were co-opted by the Hamas terror group, which rules Gaza and whose leaders have said their goal is to erase the border and "liberate Palestine".
Meanwhile, Gaza government officials announced that Egypt will open its border with Gaza for four days starting Saturday. A separate people crossing in northern Gaza remains open. The upcoming opening was framed as a humanitarian gesture ahead of the Muslim fasting month of Ramadan, which begins next week.
In Jordan, about 7,000 people participated in a "nakba" rally in an area close to the Israeli-occupied West Bank.
One man walked onto the stage with an effigy of Trump dangling from a noose.
The "March of Return", a seven-week long stint of protests, are set to climax on Nakba Day.