The billionaire political kingmakers planning to bankroll much of the 2016 presidential campaign spoke out together Sunday with blunt warnings on key issues for their respective parties.

Haim Saban, a media mogul and close Democratic ally of Hillary Rodham Clinton, criticized President Obama’s outreach to Iran, declaring that “we’ve shown too many carrots and a very small stick.”

Sheldon Adelson, a casino magnate who is likely to tap into his fortune in an effort to elect a Republican to the White House, upbraided many in the GOP for their opposition to legalizing millions of undocumented immigrants. Without a comprehensive overhaul, he said, the country would not be “the America that I’m proud to live in.”

Adelson, 81, and Saban, 70, have gained enormous political power in the new era of super PACs and unlimited contributions, and both made it clear during a rare joint appearance Sunday before an audience of several hundred Israeli Americans that they intend to assert that power during the next presidential campaign and beyond with policy demands for their candidates. In particular, they vowed to press both sides for a more hawkish approach to the Middle East.

Appearing before a new group called the Israeli American Council, both men issued a call for unity when it comes to support for the Jewish state, reminding all prospective presidential candidates of the primacy of the U.S.-Israel relationship. And they agreed that Obama and his administration have not been tough enough in protecting Israel’s interests.

In an interview with The Washington Post, Saban described the president’s relationship with Israeli Prime Minister Benjamin Netanyahu as “like oil and water.” That has fed a perception, he said, that Obama has not been a friend to Israel, although Saban said he thinks that, in reality, “there’s never been this level of cooperation with any previous president.”

Still, Saban said that he thinks Clinton would repair the relationship and that he has told her he would spend “whatever it takes” to propel her into the White House. That includes giving millions of dollars to Priorities USA, a super PAC that helped Obama in 2012 and is revving up to aid Clinton in 2016.

“I have told her and everybody who’s asked me, ‘Whatever it takes, we’re going to be there,’ ” Saban said. “I think she would be a fantastic president for the United States, an incredible world leader and one under whom I believe — deeply — the relationship with the U.S. and Israel will be significantly reinforced.”

Asked if he would press his friend Adelson to give to the pro-Clinton super PAC, Saban said, “I’ve got chutzpah, but I’m not suicidal.”

In their public remarks, Saban and Adelson found common ground in their disdain for Iran, and their fear for the danger they say that regime poses for Israel. They expressed concern about U.S. negotiations over Iran’s nuclear program.

Adelson said that Iranian fundamentalists are instructed by their religion to “wipe out all infidels” and that “wiping out the Jews would be a down payment on that.”

Referring to U.S. engagement with Iran, he said: “I would not just talk. I would take action.”

Saban said that fundamentalist Iranians represent a real threat. If necessary to defend Israel, and as a last resort, he added, “I would bomb the living daylights out of the sons of bitches.”

Saban endorsed a bill from Sen. Lindsey O. Graham (R-S.C.), who addressed the group on Saturday night, that would subject any Iranian nuclear deal to congressional approval. Saban said a system of checks and balances with the Obama administration on foreign policy is critical.

Saban used dark humor to spin last week’s Democratic wipeout in the midterm elections. “Do you know the movie ‘Life of Brian,’ by Monty Python? While they’re being crucified, they’re singing, ‘Always look at the bright side of life,’ ” Saban said in the interview, playfully humming along as he recited the movie tune.

Adelson declined an interview request. As he entered the ballroom, a Post reporter asked him about the election results. “How deep do you want to fish?” Adelson replied before moving along.

Onstage, Shawn Evenhaim, the national chairman of the Israeli American Council, posed provocative questions to both billionaires. Adelson sat to Evenhaim’s right, Saban to his left — although, as Saban joked, “there’s no right or left when it comes to Israel.”

In their hour-long discussion, Saban and Adelson had few disagreements, but one concerned how Israel engages with Palestinians. Saban said Israel has no choice but to negotiate with the Palestinians, whose numbers in the region roughly equal those of Israeli Jews.

“What is Israel to do with these 6 million people?” Saban asked. “It is not about granting the Palestinian state. It’s about securing the future of a democratic Israel.”

But Adelson rejected the feasibility of a two-state solution.

“Newt Gingrich was right: The Palestinians are an invented people,” Adelson said, referring to a controversial statement made by the former Republican House speaker whose failed 2012 presidential campaign Adelson heavily funded.

Evenhaim asked the men whether they think the news media are biased against Israel. Saban said they are but cited two exceptions: Fox News Channel and the Wall Street Journal. He joked to Adelson that they should have bought The Post together.

“I wish that Jeff Bezos hadn’t bought The Washington Post,” Saban said, referencing the Amazon.com founder who purchased The Post a year ago. “For $250 million — bupkis — he stole it.”

Adelson countered, “Why don’t you and I go after the New York Times?” Saban said that he has “tried over and over to buy it” but that the family-owned Times is not for sale. Adelson quipped, “There is only one way to fight it: money.”

A reminder of Adelson and Saban’s outsize influence came when Evenhaim wrapped up Sunday’s event. “After the election in 2016,” he told them, “one of you will get me a private tour of the White House.”