Israeli Prime Minister Benjamin Netanyahu gave interviews to three American TV networks Sunday, criticizing the Iran deal. (Israeli Government Press Office/EPA)

President Obama made a detailed case Sunday for a new framework agreement on Iran’s nuclear program, calling it a “once-in-a-lifetime opportunity to see whether or not we can at least take the nuclear issue off the table” and potentially bring regional stability to the Middle East.

Obama’s comments were part of a major sales pitch launched by the administration Sunday in an effort to marshal public support for the tentative pact, even as Israeli Prime Minister Benjamin Netanyahu and congressional Republicans took to the airwaves to blast the accord.

In a wide-ranging interview with New York Times columnist Thomas Friedman, Obama discussed his reasons for pursuing an agreement with Iran, the nation Netanyahu described Sunday as “the preeminent terrorist state of our time.” And Obama spoke in blunt terms about how it has been “personally difficult” for him to be perceived as anti-Israel as relations between his administration and Netanyahu’s have become visibly strained.

“There has to be the ability for me to disagree with a policy on settlements, for example, without being viewed as . . . opposing Israel,” Obama said in the interview. “But this has been as hard as anything I do, because of the deep affinities that I feel for the Israeli people and for the Jewish people. It’s been a hard period.”

Obama said he understood why Netanyahu had reservations about the deal, given the fact that Israel was more vulnerable to an Iranian attack than the United States. Alluding to the Holocaust, Obama added that he also recognizes “Israel’s belief that given the tragic history of the Jewish people, they can’t be dependent solely on us for their own security.”

But he said the United States would stand by Israel if it were “attacked by any state” and said he had a straightforward message to the Israeli people: “There is no formula, there is no option, to prevent Iran from getting a nuclear weapon that will be more effective than the diplomatic initiative and framework that we put forward — and that’s demonstrable.”

The fight to shape public perceptions of the deal could have major implications for its survival, with congressional Republicans pushing for the right to accept or reject any final pact. The White House has warned that the president would veto legislation the Senate Foreign Relations Committee is poised to take up this month that would withhold sanctions relief for Iran under the final deal until lawmakers had a 60-day ­period to review and vote on it.

Netanyahu appeared Sunday on three U.S. networks, while U.S. Energy Secretary Ernest Moniz and deputy national security adviser Ben Rhodes also appeared on Sunday news shows. Multiple Republican and Democratic senators also delivered their assessments of the framework agreement — largely divided along party lines — in on-air interviews.

For the most part in the Times interview — recorded Saturday and released Sunday afternoon — Obama addressed his remarks to a domestic audience: to his critics, such as congressional Republicans, and traditional Democratic supporters who have reservations about the deal, such as American Jews. He raised the prospect of striking a deal with Senate Foreign Relations Committee Chairman Bob Corker (R-Tenn.), who plans to take up the legislation that would withhold sanctions relief for Iran.

Corker “is somebody who is sincerely concerned about this issue and is a good and decent man, and my hope is that we can find something that allows Congress to express itself but does not encroach on traditional presidential prerogatives — and ensures that, if in fact we get a good deal, that we can go ahead and implement it,” the president said.

Speaking on “Fox News Sunday,” Corker identified multiple “red flags” in the framework agreement, including what elements would be considered before international sanctions on Iran are lifted and the uncertainty surrounding what process would be in place for the International Atomic Energy Agency to conduct inspections.

Obama needs to convince both lawmakers and the people they represent that finalizing the agreement serves the nation’s ­interest, Corker said, adding: “There’s a lot of water that needs to go under the bridge here. Many, many details are unknown at this point.”

Gary Samore, a former nuclear arms adviser to President Obama, said in an interview with The Washington Post that some sort of compromise between the White House and lawmakers about congressional input is well within reach. Lawmakers will ultimately have to vote to lift some sanctions against Iran as part of a final deal, he noted, and they can overturn any agreement with a two-thirds vote.

“Congress, after all, does has a role in this,” said Samore, who is the executive director for research at the Belfer Center for Science and International Affairs at Harvard University’s Kennedy School of Government. But he said it was unlikely that administration officials would give Congress the power to scuttle any agreement with a simple majority vote. “Why would they give away the advantage the Constitution gives them?”

Obama’s aides on Sunday made the case for pursuing a final accord with the Iranians, working to counter the political onslaught they are facing in the halls of Congress and in Jerusalem. “We have blocked all of these pathways to a bomb, and we should also emphasize this is not a 10-year deal,” Moniz, one of the deal’s key negotiators, said on CBS’s “Face the Nation.” “This is a long-term arrangement.”

But Netanyahu called it “a historically bad deal” on NBC’s “Meet the Press,” suggesting it would lead to both a conventional and nuclear arms race in the Middle East. “I think this deal is a dream deal for Iran and a nightmare deal for the world,” the Israeli leader said.

Netanyahu argued that the United States could have brokered a better deal and still has the option of doing so by ratcheting up the pressure of sanctions against Iran. “I think that what they don’t accept today, they can accept tomorrow,” he said in an interview on ABC’s “This Week.”

Sen. Lindsey O. Graham (R-S.C) echoed that point on “Face the Nation,”calling the president “a flawed negotiator” and suggesting that without the “baggage of Obama,” the next president — regardless of party — would be able to secure a stronger deal.

But the administration appears to have made some headway with Senate Democrats, some of whom had said in recent weeks they backed the proposal by Corker and Sen. Robert Menendez (D-N.J.) to hold an up-or-down vote on any pact over Iran’s nuclear capability.

Sen. Dianne Feinstein (Calif.), the top Democrat on the Senate Intelligence Committee, said on CNN’s “State of the Union” that the nuclear framework was “a better agreement, candidly, than I thought it was ever going to be” and that she would not support Corker’s bill in its current form.

Sen. Chris Murphy (D-Conn.), on “Meet the Press,” noted that other sanctions — including over Iran’s ballistic missile program, the country’s support for terrorism and record on human rights — will remain in place even if the framework agreement is finalized.

Obama emphasized that any accord was not contingent on trusting the Iranians or a change in their controversial tactics.

“Even for somebody who believes, as I suspect Prime Minister Netanyahu believes, that there is no difference between Rouhani and the supreme leader and they’re all adamantly anti-West and anti-Israel and perennial liars and cheaters— even if you believed all that, this still would be the right thing to do,” he said. “It would still be the best option for us to protect ourselves. In fact, you could argue that if they are implacably opposed to us, all the more reason for us to want to have a deal in which we know what they’re doing and that, for a long period of time, we can prevent them from having a nuclear weapon.”

White House officials made it clear they had given up on the idea of winning over Netanyahu, who made opposing the ongoing nuclear talks a central part of his recent and successful reelection bid. “I think that we’re not going to convince Prime Minister Netanyahu,” Rhodes said on CNN’s “Fareed Zakaria GPS.” “Frankly, he’s disagreed with this approach since before the joint plan of action, the first interim agreement that was reached with Iran.”

More broadly, Obama said Americans were “powerful enough” to test the proposition of engaging with longtime enemies such as Cuba and Iran in an effort to integrate them more closely into the world order.

“And if it turns out that it doesn’t lead to better outcomes, we can adjust our policies,” he said in the interview, referring to Cuba. “The same is true with respect to Iran, a larger country, a dangerous country, one that has engaged in activities that resulted in the death of U.S. citizens. But the truth of the matter is, Iran’s defense budget is $30 billion. Our defense budget is closer to $600 billion. Iran understands that they cannot fight us. . . . You asked about an Obama doctrine. The doctrine is: We will engage, but we preserve all our capabilities.”

Michelle Ye Hee Lee and Carol Morello contributed to this report.