Both opposed the deal on Iran's nuclear program, while Saudi officials spoke about their anger that President Barack Obama didn't follow through on a commitment to punish Syria if it crossed the "red line" of chemical weapons use.
Turki said the "strategic relationship with the U.S. will remain, from the Saudi point of view," but suggested it needed rethinking.
"There needs to be a re-evaluation and recalibration of the relationship," he said.
Amidror said that while the "Palestinian issue" was a major difference between Israel and the United States, there is "no substitute for the United States of America in the Middle East."
Those "who think other countries can do what the United States used to do is a big mistake," he said. And he indicated that he understood the Obama administration's attempts to recalibrate its ties to the Middle East.
Both men made it clear that their countries will take steps if they see any erosion of the Iran deal they so forcefully opposed.
Turki said "all options" would be on the table if Iran moves toward a bomb, "including the acquisitions of nuclear weapons, to face whatever eventuality might come from Iran."
Officials from the kingdom, which is party to the nuclear nonproliferation treaty, have raised that possibility in the past. However, they have more strongly stressed the need for the Middle East to be a "weapons of mass destruction free zone," as Turki did at the event.
Amidror said he expected that Iran will move to build a bomb "toward the end of the agreement," which limits research, development and enrichment over 10 to 15 years, if it doesn't violate it first
"In principle, the Iranians can go nuclear and from the Israeli point of view, this is a threat to existence," Amidror said. "We will not let this happen."
The two men, sitting side by side on a stage, generally impassive while the other spoke, sparred gently over the long-running Israeli-Palestinian conflict.
Arab cooperation with Israel would improve, Turki said, if it could resolve its decadeslong disagreement with the Palestinians.
"Cooperation between Arab countries and Israel in meeting threats, from wherever they come, whether Iran, is better fortified if there is peace between the Arab nations and Israel," he said
The Saudi prince returned to the issue repeatedly, criticizing Israel's presence in the West Bank and tying it to a wider Mideast peace.
"There has to be a lifting of the occupation," Turki said. "The Palestinians have to have their own country."
But Amidror said it was the Palestinians who were sabotaging the process. He argued it was a mistake for the Arab world to give the Palestinians the "key" to unlocking the relationship with Israel, since that effectively blocked progress.
Arab states, Amidror told Turki, should "cooperate with Israel instead of dictating" to it. He urged regional leaders to "think outside the box" and suggested the Arab world form an "umbrella of cooperation" on Palestinian issue to help move negotiations along.
(CNN)