Clashes erupted in the occupied West Bank and over the Israeli-Gaza border, where one Palestinian was killed.
Tensions are high in the wake of Mr Trump's announcement. His policy shift was hailed by Israel but condemned across the Arab and Islamic world.
The UN's Middle East envoy warned of a risk the conflict would escalate.
"There is a serious risk today that we may see a chain of unilateral actions, which can only push us further away from achieving our shared goal of peace," Nickolay Mladenov told an emergency UN Security Council meeting, by videocall from Jerusalem.
He called on all parties to engage in "constructive dialogue" and "reign in radical elements".
While the meeting was going on, the Israeli army said it had intercepted a rocket launch from Gaza, but there had been "no casualties and no damage".
Western allies of the US have disavowed Mr Trump's move, which reversed decades of US neutrality on the status of Jerusalem.
Israel has always regarded Jerusalem as its capital, while the Palestinians claim East Jerusalem - occupied by Israel in the 1967 war - as the capital of a future Palestinian state.
The US became the first country to recognise Jerusalem as Israel's capital since the foundation of the state in 1948.
US Secretary of State Rex Tillerson has said it could take two years before the US embassy is relocated from Tel Aviv.
Where has there been violence?
In the West Bank, Israeli forces clashed with Palestinians in the cities of Bethlehem, Ramallah, Hebron and Nablus, as well as smaller locations.
Television pictures from Bethlehem showed water cannon or so-called skunk water being used against stone-throwing protesters.
Clouds of tear gas and thick, black smoke from burning tyres filled the air. There were also reports of rubber bullets being fired by troops. Similar scenes were reported in other places where there were confrontations.
Israel had deployed extra battalions to the West Bank in anticipation of violence after Palestinian leaders called for protests after Friday prayers.
In East Jerusalem there were scuffles as police pushed back hundreds of demonstrators outside the Old City. The ancient walled area, containing contentious holy sites, is historically a flashpoint for violence.
At least 217 Palestinians were wounded in the confrontations in the West Bank and East Jerusalem, Palestinian medics said. A 30-year-old Palestinian was killed and dozens of others injured in Gaza after Israeli forces opened fire after protesters threw stones at army posts on the border. Elsewhere, demonstrations against Mr Trump's announcement have spread.
Thousands of pro-Palestinian protesters held noisy demonstrations in Jordan, Egypt, Iraq, Turkey, Tunisia and Iran.
Further afield, protesters rallied in Malaysia, Bangladesh, Pakistan, Afghanistan, Indian-administered Kashmir and Indonesia, the world's largest Muslim-majority country.
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