"The whole purpose is to just get everybody on one page rather than throwing books around," said Israel, who added that he was expecting a "candid conversation" about how to "move forward."
CNN first reported the plan for the dinner. A person familiar with the dinner plan who was granted anonymity to describe the private gathering told The Washington Post that four other House Democrats attended: Reps. Ruben Gallego (Ariz.), Kathleen Rice (N.Y.), Gwen Graham (Fla.) and Seth Moulton (Mass.).
Israel said he initiated the dinner. "Israel to Israel, I call it," said the congressman.
In an interview after the dinner, Israel said that "75 percent" of it "was substantive conversation about a potential nuclear deal with Iran." The other 25 percent, he said, focused "on the optics of the past month."
"We're going to have to find a way to manage the discourse," said Israel.
The dinner meeting came on the same day a top aide to Obama used a speech before a liberal Jewish advocacy group to express the administration's continued frustration with Netanyahu.
The Israeli leader, on the eve of his reelection last week, vowed that he would not allow a Palestinian state to be established during his time in office, but then backtracked on those remarks after securing his fourth term. White House Chief of Staff Denis McDonough on Monday described Netanyahu's remarks in a speech at the annual J Street National Conference in Washington as "so very troubling."
McDonough said that "an occupation that has lasted for almost 50 years must end, and the Palestinian people must have the right to live in and govern themselves in their own sovereign state."
McDonough's speech was the latest in a series of calculated swipes at the Israeli leader from the White House, which last week derided Netanyahu's “cynical, divisive election day tactics.” In an interview with the Huffington Post, Obama said that he told Netanyahu that his pre-election remarks had made it hard to conceive of "a path where people are seriously believing that negotiations are possible."
McDonough on Monday sounded a similar theme. "We cannot simply pretend that those comments were never made, or that they don’t raise questions about the prime minister’s commitment to achieving peace through direct negotiations," he said.
Much of McDonough's address focused on the status of negotiations with Iran over its nuclear program and the importance of securing a negotiated peace between Israelis and Palestinians. The Obama administration has set a March 31 deadline for the outlines of a negotiated settlement that would prevent Iran from developing a nuclear weapon. With time running out, McDonough's remarks suggested that a deal was close and sought to ease the concerns of Republican skeptics in Congress.
"If a deal is reached, we will share the details and technical documents with Congress, at which point we welcome a full debate," McDonough said. "Everyone from the president on down will aggressively seek congressional and public support for any deal. There will surely be voices on all sides ... because a good deal is the best way to reach our shared goal — preventing Iran from gaining a nuclear weapon."
Rep. Israel said McDonugh's comments didn't come up at the dinner discussion with the Israeli ambassador.
House Speaker John A. Boehner (R-Ohio) is planning to visit Israel in the coming weeks. The planned trip comes after Boehner angered many Democrats by inviting Netanyahu to address a joint meeting of Congress on March 3.
Netanyahu, like Boehner and many Republicans, opposes the Obama administration's efforts to strike a nuclear deal with Iran.
Rep. Israel said he thinks Boehner's trip can be a positive one.
"The more people in Congress who can go to Israel, the better," said Israel.