Speaking on Monday, the last day of the campaign, Donald Trump told his Florida audience: "Barack Obama was the worst thing that ever happened to Israel."

President-elect Trump was echoing a theme he has returned to time and again: that he will be a much stauncher supporter of Israel than the current administration.

In the first debate with Hillary Clinton in September, in which Mr Trump criticised the administration's policy on Iran, he said: "I met with Bibi Netanyahu the other day, believe me, he's not a happy camper."

If his words are an accurate guide to his actions in office, in January Israel will be the beneficiary of the most sympathetic American president ever. But some in Jerusalem fear that President Trump may be too right-wing even for Benjamin Netanyahu. He has promised to "get tough" on Iran and ensure that it is held to the letter of the nuclear deal. Unlike some other Republicans, however, he has not promised to cancel the deal.

On the Israel-Palestinian issue, he and his close advisers have been even more emphatic. They removed from the Republican party's official platform any mention of the two-state solution or the Palestinians.

In many quarters of Israel's right wing, the response to his victory on Wednesday morning was ecstatic. Education Minister and leader of the Jewish Home party, Naftali Bennett, welcomed the election result, saying: "Trump's victory is a tremendous opportunity for Israel to immediately announce its intention to renege on the idea of establishing Palestine in the heart of the country."

Jerusalem Mayor Nir Barkat was also delighted, saying he expected Mr Trump to become the first US president to live up to his election promise to move America's embassy from Tel Aviv to Jerusalem. "I'm certain that throughout your term you will continue strengthening the status and sovereignty of Jerusalem as Israel's capital and move the US embassy to the city," he said in his congratulations.

Mr Netanyahu was less effusive. "President-elect Trump is a true friend of the state of Israel," he said. "We will work together to advance security, stability and peace in our region. The strong connection between the United States and Israel is based on shared values, shared interests and a shared destiny. I'm certain that President-elect Trump and I will continue to strengthen the unique alliance between Israel and the United States, and bring it to new heights." The same remarks could equally have been used if Mrs Clinton had won.

Later in the day, the two men spoke over the phone, Mr Trump inviting the prime minister to visit him in Washington "at the first opportunity".

For Mr Netanyahu, who has spent an accumulated decade in office in tense relationships with two Democratic presidents - Bill Clinton in his first term and Barack Obama since returning to power in 2009 - it will be the first time as prime minister that he is greeted by a Republican president.

But Mr Trump is probably not the kind of Republican he was hoping for. While many in the prime minister's camp, especially his American patron, the casino mogul Sheldon Adelson, were openly rooting for Mr Trump, the Israeli PM scrupulously remained on the fence.

Mr Netanyahu is, by ideology, a Republican but a number of people close to him have said in recent weeks that he is not enamoured with Mr Trump. According to one: "Bibi has a difficult history with the Clintons, from the days of his first term during Bill Clinton's presidency, but he knows Hillary and what she is capable of doing. Trump may claim to be supporting Israel to the hilt but he is an unknown quantity, an unpredictable kind of guy, and Bibi is risk-averse and hates uncertainty."

The prospect of a Trump presidency could well cause trouble in Mr Netanyahu's coalition as well.

The more right-wing elements in his government will now be clamouring for Israel to take advantage of what they expect to be a more favourable diplomatic climate with less international pressure, and resume wide-scale building in east Jerusalem and the West Bank.

For the prime minister, who is anxious to safeguard the status-quo with the Palestinian Authority and the security coordination, this will not be the best moment to rock the boat.