President Donald Trump, who on Tuesday presided over the signing of normalization agreements between Israel and two Gulf Arab states, says several other nations are close to following the example of Bahrain and the United Arab Emirates.

He also expressed confidence that Saudi Arabia will, when the time is right, join the process of fully normalizing relations with the Israelis, Reuters reported.

Trump told reporters at the White House that the Kingdom is among several countries he believes are on the verge of opening diplomatic ties with Tel Aviv, according to a Turkish news agency reporting on the ceremonial signing, Anadolu Agency. Similar remarks about the Saudis following "at the right time" were reported by The Times of Israel.

I spoke with the King of Saudi Arabia. We had a great conversation, and I think positive things will happen there, too. He’s a great gentleman. And the Crown Prince — we spoke with the Crown Prince," Trump said, in remarks transcribed by the White House.

"So we’ve made tremendous strides. And this is peace in the Middle East without blood all over the sand. I say it: Right now, it’s been blood all over the sand for — for decades and decades and decades. That’s all they do, is they fight and kill people, and nobody gets anything. And this is — this is strong peace, really strong peace, far — and it’s a different way."

The president also increased the number of nations he says are close to following in the steps of the initial two Arab Gulf nations after initially talking of five or six prospective signatories.

"We’ll have 7 or 8 or 9. We’re going to have a lot of other countries joining us, including the big ones," he said.

For its part, Saudi Arabia said on Tuesday it stands by the Palestinian people and supports all efforts aimed at reaching a just and comprehensive solution to the Palestinian issue, according to a cabinet statement.

"The cabinet notes that the kingdom stands by the Palestinian people and supports all efforts aimed at reaching a just and comprehensive solution to the Palestinian issue that enables the Palestinian people to establish their independent Palestinian state on the 1967 borders, with East Jerusalem as its capital, in accordance with international legitimacy decisions and the Arab Peace Initiative," the statement said.

To many Mideast experts, gaining Saudi support would be a major coup. “Saudi Arabia is the game,” said Bruce Riedel, a former CIA officer who specializes in the Gulf kingdom, as reported by Financial Times. But with King Salman “a true believer in the Palestinian cause" of an independent state, the path ahead won't be a simple one.

The new agreements, The Times of Israel noted, don't speak to the decades-long Israeli-Palestinian conflict. While the UAE, Bahrain and other Arab countries support the Palestinians, the Trump administration has persuaded the signatories not to let that conflict keep them from having normal relations with Israel.

And, experts also note, Riyadh, with the Arab world's biggest economy and many of its holiest sites, has provided substantial financial support to cash-strapped Bahrain and likely offered a behind-the-scenes nod to Bahrain's participation in the new agreements, even if Saudi Arabia has itself so far resisted. The Saudis are also thought to have been cultivating behind-the-scenes ties with the Jewish state to contend with their common nemesis in the region, Iran.

Indeed, in one recent sign of the kingdom's cooperation with Israel, is has agreed to allow UAE flights to Israel to overfly its territory.

“This is what I would call ‘alternative normalization’,” Ryan Bohl, of the US geopolitical think tank Stratfor, told AFP.

“Though Saudi will remain slower on this path, it’s clear the kingdom is open to normalization and will explore growth in the relationship through increasingly public, though likely indirect, ties.”