Jerusalem (CNN) On the campaign trail, Donald Trump the candidate promised to recognize Jerusalem as the undivided capital of Israel -- a move that would upend decades of US policy.

Now that he's the President-elect, Israel's right wing is thrilled and is calling on Trump to relocate the American embassy f rom Tel Aviv to Jerusalem as soon as he takes office.

Jerusalem Mayor Nir Barkat commended Trump's position on Jerusalem and said the status of the city is not open for negotiation. "The role of the city of Jerusalem will never change," Barkat said the day after the elections. "It has to be under the sovereignty of the Jewish people. It has to play an inclusive role. It can never function as a divided city." Other right-wing politicians joined Barkat in calling on Trump to fulfill his campaign promise.

It is an often repeated -- and never fulfilled -- promise made by both Democratic and Republican presidential candidates. The Jerusalem Embassy Act of 1995 requires the US government to move the embassy to Jerusalem, but the move has been waived every six months since the law was passed. Presidents Clinton, Bush, and Obama all declined to relocate the embassy after being elected, citing national security.

Jerusalem: The most difficult question

Benjamin Netanyahu met Donald Trump at Trump Tower in New York in September.

Riyad Mansour, the Palestinian Ambassador to the United Nations, told a conference in Washington, DC on Friday: "If [the US administration moves the embassy to Jerusalem], nobody should blame us for unleashing all of the weapons that we have in the UN to defend ourselves, and we have a lot of weapons in the UN."

Jerusalem has always been the most difficult question in the Israeli-Palestinian conflict. Even after the world recognized the State of Israel in 1948, it left the final status of Jerusalem open to future negotiations. Israelis see Jerusalem as their united capital; Palestinians see East Jerusalem as the capital of a future Palestinian state.

Education Minister Naftali Bennett, leader of the right-wing Jewish Home party, said Trump's election allows Israel to fully dismiss the notion of a Palestinian state. "This is the position of the President-elect, as written in his platform, and it should be our policy, plain and simple. The era of a Palestinian state is over."

Naftali Bennett, leader of the right-wing Jewish Home party.

Prime Minister Benjamin Netanyahu's comments to the President-elect were much more measured -- he didn't mention Jerusalem or the embassy. "President-elect Donald Trump is a true friend of the State of Israel, and I look forward to working with him to advance security, stability, and peace in our region."

As the final results of the election were coming in, US Ambassador to Israel Dan Shapiro lauded the Iran nuclear deal -- vigorously opposed in Israel -- and urged Trump's administration to stick with decades of US policy. But when asked what would become of the embassy, Shapiro said, "Every government, every US administration has looked at that question, has determined that the embassy is where it should be," Shapiro said. "And I can't speculate beyond that."

Palestinians: We'll work with any president

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Palestinian leaders were much more reserved in their comments about Trump's victory. Presidential spokesman Nabil Abu Rudeineh said that the Palestinians were ready to work "with any president elected by the American people on the principle of achieving permanent peace in the Middle East based on the two-state solution", with "East Jerusalem as its capital." PLO Secretary General Saeb Erekat said a two-state solution has been a priority for Republicans and Democrats.

In an interview with the Wall Street Journal, Trump said an Israeli-Palestinian peace agreement would be the "ultimate deal" and that he'd "like to do ... the deal that can't be made. And do it for humanity's sake."

But if Trump recognizes Jerusalem as the undivided capital of Israel, it would dash the Palestinian goal of a capital in East Jerusalem, making a peace deal between Israelis and Palestinians even more remote. It would also ratchet up tensions between the US and Arab countries that want to see a Palestinian capital in East Jerusalem.

Will Trump actually fulfill his promises?

Palestinian political analyst Mahdi Abdul Hadi doubts that Trump will fulfill his campaign promise. He believes the President-elect will do what his predecessors have done for more than 20 years -- waive the embassy relocation.

"What's new?" he asks. "It's only rhetoric. It's only slogans, although it's very much symbolic to tell us, 'You Palestinians will not have a capital in Jerusalem.' Nobody can dismiss our presence in Jerusalem. We are deep-rooted here."

With Trump's advisers on Israel repeatedly promising to recognize Jerusalem as the capital of Israel, Palestinian leaders will look in a different direction in the immediate future.

Working with a group of Arab countries, the Palestinians have been drafting a UN Security Council resolution condemning Israel's settlement activity in the West Bank. The last time they tried to pass such a resolution in 2011, President Obama vetoed it, making it the only time Obama exercised the US veto power at the Security Council. This time, they hope, the US would either vote in favor of a resolution condemning settlements or, perhaps, abstain.

But the future, like so much in Jerusalem, suddenly seems uncertain.