As of Sunday, the president was still considering “a lot of different facts,” his son-in-law and top adviser, Jared Kushner, said at the Saban Forum, a conference hosted by the Brookings Institution in Washington. Kushner is also part of a team appointed by the president looking at how to achieve peace in the region.
Recognizing Jerusalem would upend decades of American policy.
Both Israel and the Palestinians claim the city as their capital. Israel annexed the eastern part of the city in 1967, after winning the territory from the Jordanians in the Six Day War. The move was not recognized by the United Nations.
But Mustafa Barghouti, a member of the Palestinian Legislative Council, described moving the embassy as a "very reckless act."
He added, "Declaring that Jerusalem is the capital of Israel would simply mean assassinating and destroying the peace process, completely."
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But all presidents since Bill Clinton have issued a waiver, saying Jerusalem's status is a matter for the Israelis and Palestinians to negotiate.
Trump signed the waiver at the last deadline in June, but the White House made clear then that he still intended to move the embassy.
Other Palestinian leaders echoed Barghouti’s comments, saying that any move by the U.S. to relocate the embassy would disqualify Washington from having a role in peace negotiations.
The move “will unleash forces that cannot be contained, inflaming sentiments and generating tensions and instability throughout the region and beyond,” Hanan Ashrawi, a member of the PLO executive committee, said in a statement.
East Jerusalem, where the Palestinians want to establish their capital, is home to some of the holiest sites in Judaism, Islam and Christianity.
Foreign embassies in Israel are largely in Tel Aviv, though some countries, including the U.S., have consulates in Jerusalem.
The Arab League secretary-general, Ahmed Aboul Gheit, said on Saturday that any action to recognize Jerusalem as Israel's capital would provoke violence.
"Taking such action is not justified ... It will not serve peace or stability, but will fuel extremism," Aboul Gheit said in a statement. "It only benefits one side; the Israeli government that is hostile to peace."
Jordan, which signed a peace treaty with Israel in 1994, also weighed in, with its foreign minister tweeting that the move would “trigger anger” across the Arab and Muslim world.
Spoke with #US Secretary of State Tillerson on dangerous consequences of recognizing Jerusalem as capital of Israel. Such a decision would trigger anger across #Arab#Muslim worlds, fuel tension & jeopardize peace efforts.
Israel has been supportive of Trump’s plan to move the embassy both now and last spring before Trump signed the first waiver.
"By validating Jerusalem as the eternal united capital of the state of Israel … he is sending an important message," Israeli's minister of communications, Ayoob Kara, said Sunday at an Cabinet meeting.
Jerusalem’s status has long been a contentious issue. A visit to the Temple Mount in 2000 by the Israeli politician Ariel Sharon prompted an outbreak of violence just prior to the second Palestinian intifada, or uprising.
This past summer, violence again erupted as Israel implemented new security measures at the entrances to Al-Asqa Mosque.
The U.S. also potentially faces legal constraints. Recognizing Jerusalem as Israel's capital without a peace deal could run afoul of U.N. Security Council resolutions that don't recognize Israeli sovereignty over the city. Washington has a veto on the council and could block any effort to declare the U.S. in violation, but any such vote risks being an embarrassment and driving a wedge between the United States and many of its closest allies.
Ron Allen, Paul Goldman and Lawahez Jabari reported from Jerusalem. Rachel Elbaum reported from London.
Ron Allen is an NBC News correspondent based in New York.
Paul Goldman is a Tel Aviv-based producer and video editor for NBC News.
Lawahez Jabari is a producer based in Tel Aviv. She has covered the Middle East conflict — on both the Israeli and Palestinian sides — for more than a decade.