Israel carried out an air strike on the Gaza Strip after a rocket was fired from the territory, with Palestinian sources reporting 10 people wounded.
In the diplomatic fallout from the deeply controversial declaration, a Palestinian official warned that president Mahmud Abbas could refuse to meet US Vice President Mike Pence on his visit to the region later this month.
The Security Council held an emergency session in New York to discuss Trump's move, which has drawn near universal condemnation, including from United Nations chief Antonio Guterres.
Five European countries on the council insisted the new US policy was not consistent with past UN resolutions, including one that considers east Jerusalem to be Israeli-occupied.
But the US ambassador to the UN, Nikki Haley, tried to assure delegates that the White House was serious about the search for peace.
"Let me again assure you, the president and this administration remain committed to the peace process," she said.
The meeting was convened by eight of the 14 non-US members of the council but was largely symbolic -- no vote on a resolution was planned, as the US has veto power.
Abbas hailed the international concern, according to a statement carried by official Palestinian news agency WAFA.
"Mahmud Abbas welcomed the international condemnation of the American decision to consider the city of Jerusalem the capital of Israel, which occurred at the United Nations Security Council," it said.
Whether violence would spread and spiral both in the Palestinian territories and elsewhere was being closely watched, with Friday marking a second day of unrest.
Palestinian Islamist movement Hamas, which runs the Gaza Strip, had called for a "day of rage" and its leader Ismail Haniya for the start of a new intifada, or uprising.
The Palestinian killed in clashes along Israel's border with Gaza was the first death linked to protests since Trump's declaration on Wednesday.
A second Palestinian in Gaza was in "very critical" condition after being shot in the head during the clashes.
The Israeli army said around 4,500 Palestinians "participated in violent riots" along the Gaza-Israel border.
It said that troops shot at "dozens" of people along the frontier, but did not specify how many were wounded.
"During the riots soldiers fired selectively towards dozens of main instigators and hits were confirmed," an English-language statement said.
On Friday evening, Palestinians in Gaza fired a rocket at Israel which was shot down by Israel's Iron Dome anti-missile system, the army said.
The Israeli military said it hit Hamas military facilities in Gaza in response to the rocket attack, while the Palestinian health ministry said 10 people wounded.
In the West Bank, thousands of Palestinians also took part in "violent riots" throughout the territory, with 28 Palestinians arrested and about 65 wounded, the army said.
It did not elaborate on the type of injuries.
'God knows where'
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".
For Jewish Israelis, the declaration is a simple recognition of reality and validation of their view that Jerusalem is their 3,000-year-old capital.
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.
Its status is perhaps the most sensitive issue in the decades-long Israeli-Palestinian conflict, and international consensus has been that it must be negotiated between the two sides.
"It's empty talk," said a 20-year-old man who gave his name only as Omar as he walked towards 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.
But while the declaration may mean little immediate concrete change, it risks setting off another round of bloodshed in the turbulent Middle East.
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 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".
'Not welcome'
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.
Mohammad Shtayyeh, a senior Palestinian official who has been involved in past peace talks, questioned what was left to negotiate.
"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.
He was due to meet the Palestinian president in the second half of December on a regional tour, but a senior member of Abbas's Fatah faction said this would not now happen.
"The American vice president is not welcome in Palestine. And President Abbas will not welcome him," Jibril Rajoub said.
Abbas has not made similar comments, and the White House is likely only to consider the meeting cancelled if he does so himself.
A White House aide said Pence "still plans to meet with Abbas as scheduled", and "believes it would be counterproductive for him to pull out of the meeting".
Grand Imam Ahmed al-Tayeb of Al-Azhar, Egypt's highest Sunni institution, has cancelled a meeting with Pence, a statement said.
