Clashes erupted in the occupied West Bank and over the Israeli-Gaza border, where one Palestinian was killed.
Overall more than 200 were hurt, Palestinian medical sources said.
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.
Western allies of the US have also disavowed the move, which reversed decades of US neutrality on the status of Jerusalem.
The UN Security Council is holding an emergency meeting.
- Anger in the West Bank and delight in West 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.
In recognising Jerusalem as Israel’s capital, the US became the first country to do so 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.
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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.
How has the international community reacted?
There has been widespread denunciation of Mr Trump’s move, especially in the Muslim world.
America’s closest Arab allies, Saudi Arabia, Egypt and Jordan, have expressed their opposition, while Egypt, Bolivia, France, Italy, Senegal, Sweden, the UK and Uruguay have called an emergency meeting of the UN Security Council on Friday to discuss the step.
- Which countries condemned Trump’s move?
Palestinian President Mahmoud Abbas said Mr Trump’s announcement was “deplorable” and a senior Palestinian official said US Vice President Mike Pence was “not welcome in Palestine” during a planned visit to the region later this month.
Israel’s arch-foe Iran accused Donald Trump of trying to provoke a war, while the Iran-backed Hezbollah movement in Lebanon called on the Muslim and Arab world to support a new intifada.
Israel itself has hailed the announcement as historic. Prime Minister Benjamin Netanyahu called it a “courageous and just decision”, while some 250 Israeli rabbis, including the chief rabbi of the Sephardi Jewish community, signed a letter thanking Mr Trump.
Why does Trump’s announcement matter?
Jerusalem is of huge importance to both Israel and the Palestinians. It contains sites sacred to the three major monotheistic faiths – Judaism, Islam and Christianity.
Israel occupied the eastern sector – previously occupied by Jordan – in 1967, and annexed it in 1980, but the move has never been recognised internationally.
Some 330,000 Palestinians live in East Jerusalem, along with about 200,000 Israeli Jews in a dozen settlements there. The settlements are considered illegal under international law, though Israel does not regard them as settlements but legitimate neighbourhoods.
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According to the 1993 Israel-Palestinian peace accords, the final status of Jerusalem is meant to be discussed in the latter stages of peace talks.
The last round of talks between Israel and the Palestinians broke down in 2014 and while the US is formulating fresh proposals.