Leaders from within the Muslim world and from the wider international community were swift to criticise the move, and some warned of the potential for violence and bloodshed as a result.
Mr Trump also approved moving the US embassy from Tel Aviv to Jerusalem, making America the first country in the world to officially recognise Jerusalem as Israel’s capital.
The status of Jerusalem lies at the heart of the long-running Israeli-Palestinian conflict, as the Palestinians claim East Jerusalem as the capital of their future state.
White House officials have said Mr Trump’s decision is a “recognition of current and historic reality” but is not a political statement, and will not change the physical and political borders of Jerusalem.
President Mahmoud Abbas said the decision was tantamount to the United States “abdicating its role as a peace mediator” after a decade of sponsoring the Israeli-Palestinian peace process.
“These deplorable and unacceptable measures deliberately undermine all peace efforts,” he said in a pre-recorded speech on TV.
He insisted that Jerusalem was the “eternal capital of the state of Palestine”.
Palestinian Islamist group Hamas chief Ismail Haniyeh said: “Our Palestinian people everywhere will not allow this conspiracy to pass, and their options are open in defending their land and their sacred places.”
A spokesman for the group said the decision would “open the gates of hell on US interests in the region”.
Israel’s Prime Minister Benjamin Netanyahu said President Trump’s announcement was a “historic landmark”.
He called the US president’s decision “courageous and just”.
The Israeli prime minister said the speech was “an important step towards peace, for there is no peace that doesn’t include Jerusalem as the capital of the State of Israel”.
He said that the city had “been the capital of Israel for nearly 70 years”.
Education Minister Naftali Bennett also hailed the decision, saying “the United States is adding another brick to the walls of Jerusalem, to the foundation of the Jewish nation”, and urged other nations to follow Mr Trump’s lead.
The Turkish Foreign Minister Mevlut Cavusoglu said the decision was “irresponsible.”
He wrote on Twitter that “the decision is against international law and relevant UN resolutions”.
Saudi Arabian media say King Salman told Mr Trump by telephone on Tuesday that the relocation of the embassy or recognition of Jerusalem as Israel’s capital “would constitute a flagrant provocation of Muslims, all over the world”.
His views were echoed by President Abdul Fattah al-Sisi of Egypt, who warned against “complicating the situation in the region by introducing measures that would undermine chances for peace in the Middle East”.
The Arab League called it “a dangerous measure that would have repercussions” across the region, and also questioned the future role of the US as a “trusted mediator” in peace talks.
Iran said the decision risked a “new intifada”, or uprising. Its foreign ministry said the US had clearly violated international resolutions.
Meanwhile, Jordan’s King Abdullah called for joint efforts to “deal with the ramifications of this decision” and a Jordanian government spokesman said Mr Trump was violating international law and the UN charter.
Lebanon’s president Michel Aoun said the peace process would be set back decades, while Qatar’s foreign minister said the move was “a death sentence for all who seek peace”.
Pope Francis said: “I cannot silence my deep concern over the situation that has emerged in recent days. At the same time, I appeal strongly for all to respect the city’s status quo, in accordance with the relevant UN resolutions.”
The Secretary General of the United Nations, Antonio Guterres, said President Trump’s statement “would jeopardise the prospect of peace for Israelis and Palestinians”.
Mr Guterres said Jerusalem was “a final status issue that must be resolved through direct negotiations between the two parties”.
Such negotiations must take “into account the legitimate concerns of both the Palestinians and the Israeli sides,” he said.
The European Union called for the “resumption of a meaningful peace process towards a two-state solution” and said “a way must be found, through negotiations, to resolve the status of Jerusalem as the future capital of both states, so that the aspiration of both parties can be fulfilled”.
French President Emmanuel Macron said Mr Trump’s decision to recognise Jerusalem as Israel’s capital was “regrettable”.
He called efforts for “avoid violence at all costs.”
Both China and Russia also expressed their concern that the move could lead to an escalation of tensions in the region.
UK Prime Minister Theresa May said the UK government disagreed with the US decision which was “unhelpful in terms of prospects for peace in the region”.
In a statement she said: “The British embassy to Israel is based in Tel Aviv and we have no plans to move it.
“Our position on the status of Jerusalem is clear and longstanding: it should be determined in a negotiated settlement between the Israelis and the Palestinians, and Jerusalem should ultimately be the shared capital of the Israeli and Palestinian states. In line with relevant [UN] Security Council Resolutions, we regard East Jerusalem as part of the Occupied Palestinian Territories.”
German Chancellor Angela Merkel’s spokesman said on Twitter that Berlin “does not support this position because the status of Jerusalem can only be negotiated within the framework of a two-state solution”.
BBC contributed to this report.