Diplomatic fallout from the deeply controversial declaration also continued, with suggestions Palestinian president Mahmud Abbas could refuse to meet US Vice President Mike Pence on his visit to the region later this month.
The UN Security Council was meeting today in an emergency session to discuss Trump's move, which has drawn near universal condemnation, including from United Nations Secretary-General Antonio Guterres.
Whether unrest would spread and spiral both in the Palestinian territories and elsewhere in the region was being closely watched, with Friday marking a second day of unrest.
The Palestinian killed in clashes along Israel's border with the Gaza Strip was the first death linked to protests since Trump's declaration on Wednesday.
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A second Palestinian in Gaza was in "very critical" condition after being shot in the head during the clashes.
The Israeli army confirmed it had shot two people along the Gaza border, accusing them of being "main instigators" of "violent riots."
Dozens of people were wounded from rubber bullets or live fire in Gaza and the West Bank, according to Palestinian officials.
Palestinians in some areas set tyres alight while throwing stones and firebombs at Israeli forces, who responded with tear gas and rubber bullets.
Police said more than 50 people were arrested in the West Bank.
Tens of thousands of people also took to the streets of Muslim and Arab countries across the world in protest, including in Jordan, Turkey and Malaysia.
Trump's announcement has been met by a worldwide diplomatic backlash, though Israeli Prime Minister Benjamin Netanyahu has lavished praise on the president and called the declaration "historic."
Trump said his defiant move - making good on a 2016 presidential campaign pledge - marks the start of a "new approach" to solving the Israeli-Palestinian conflict.
But many analysts question how a fair peace process could be possible by granting such a major Israeli demand while seeming to require nothing in return.
Israel has long claimed all of Jerusalem as its undivided capital, while the Palestinians see the eastern sector of the city as the capital of their future state.
"It's empty talk," said a 20-year-old man who only gave his name as Omar as he walked toward the Al-Aqsa mosque, Islam's third-holiest site and located in Jerusalem's Old City.
"No matter what happens, we know Jerusalem is the capital of Palestine, not of Israel. Israel is an occupier."
Trump's declaration and intention to move the US embassy from Tel Aviv to Jerusalem are moves that may help him domestically since they were long-sought by US evangelical Christian and right-wing Jewish voters -- key parts of his electoral base and important financial donors.
EU diplomatic chief Federica Mogherini said the decision could take the region "backwards to even darker times".
Muslim and Middle Eastern leaders, including key US allies, have expressed increasing alarm over Trump's decision to break with decades of precedent with unpredictable consequences.
Turkish President Recep Tayyip Erdogan said it would put the region in a "ring of fire".
Palestinian leaders have been so outraged that they have argued it disqualifies the United States from its traditional role as peace broker in the Middle East conflict.
"If these are the signs of the ultimate deal, God knows what the deal is going to be," he said, referring to Trump's pledge to reach an Israeli-Palestinian peace agreement.
"Maybe the expulsion of the Palestinians -- God knows where."
The declaration is sure to weigh heavily on Pence's upcoming visit.