The Israeli army said Hamas-led protesters tried to plant bombs and attacked the border fence.
Israel has dropped leaflets warning Palestinians not to act in accordance with the wishes of Hamas, a US-designated terrorist organization that seeks to destroy Israel, by joining in the protests.
The United Nations said Israel's actions are "outrageous human rights violations".
National Party leader Simon Bridges said the case could be made for opening the new embassy, in terms of the United States "standing on its rights".
Canada also called on "all parties to the conflict" to "ensure civilians are protected".
"These are things that were negotiated between Palestinian and Israeli parties in the past that we would leave this as a neutral space until we have reached that place in our conflict where we can discuss this, and unfortunately western powers have not allowed this peace to remain and have inflamed the situation even more".
The decision to move the us embassy from Tel Aviv to Jerusalem was viewed as a de facto acceptance of Israel's claim to Jerusalem, half of which had been viewed as the future capital of a Palestinian state if a two state solution is negotiated.
Several countries, including Egypt, Turkey, Qatar and Iran directly blamed Israel for Monday's violent clashes. But Monday's protests, which took place as the USA opened the doors of its new embassy, were the largest of the past month, and the worst violence in years.
President Donald Trump sent a video message to the event, saying Israel had the "right to determine its own capital".
Kuwait called for an emergency UN Security Council meeting on Tuesday to address the violence.
"This is a hotly contested issue within that peace process and as we've seen the results of the protest along the border of Gaza have been devastating".
Earlier, a warplane and tank targeted two other Hamas posts in response to what it said was fire toward its forces by Hamas.
Also Monday, White House deputy press secretary Raj Shah defended the administration's choice to tap Texas evangelical pastors Robert Jeffress and John Hagee, to deliver a blessing at the Jerusalem ceremony, despite their past inflammatory remarks about other religions.
Around 50 or so protesters gathered beside the U.S. Embassy in Ottawa Monday May 14, 2018.
After Trump's announcement in December, India had voted with the majority in favour of the United Nations General Assembly resolution rejecting the USA recognition of Jerusalem as the capital of Israel.