WHEN Shaul Mofaz took over as head of the opposition in Israel this week — having defeated Tzipi Livni to lead the Kadima Party — it was seen as further evidence of the country’s rightward shift. A former military chief of staff and defense minister, Mr. Mofaz was dismissed by many as a pale shadow of Prime Minister Benjamin Netanyahu, a hawk who would try to join the governing Likud coalition.

So it was surprising to enter the Kadima headquarters on a gritty industrial block of this central Israeli town for an interview this week with Mr. Mofaz and hear him detail an agenda more typically associated with the left.

He said Mr. Netanyahu’s focus on Iran’s nuclear program had distracted attention from more important priorities, like making peace with the Palestinians, ending settlement building in much of the West Bank and reducing the country’s socioeconomic inequality. Let President Obama handle Iran, he said. We can trust him.

“I intend to replace Netanyahu,” Mr. Mofaz, 63, said in the party chairman’s office, so new to him that behind his desk there was still a poster for Ms. Livni. “I will not join his government.”

Then: “The greatest threat to the state of Israel is not nuclear Iran,” but that Israel might one day cease to be a Jewish state, because it would have as many Palestinians as Jews. “So it is in Israel’s interest that a Palestinian state be created.”

Mr. Mofaz said that Israel’s alliance with Washington was its greatest strategic asset, and that aligning Israeli policy more with Washington was necessary. Also, he said, Mr. Netanyahu has been talking too much about Iran. If the time comes when only an attack can stop Iran’s nuclear program, and “God forbid the American president decides not to attack,” he will support Mr. Netanyahu in such a move, he said. But he does not expect that to happen.

Of medium height and solid build, bald and generally unsmiling, Mr. Mofaz is often described in shades of gray. He will never light up a room; he is not much of a storyteller, either.

And polls indicate that if elections were held now (they are not due before the fall of 2013), Mr. Netanyahu would crush him. When Mr. Mofaz declared victory over Ms. Livni in the Kadima primary, commentators spent most of their energy analyzing her fall, concluding that she lacked leadership qualities and failed to glad-hand her supporters and challenge Mr. Netanyahu.

But since then, with Mr. Mofaz now in charge of Kadima, the party with the largest number of seats in Parliament, there has been a strain of discussion summed up by an essay in the newspaper Maariv under the headline “Don’t Underestimate Mofaz.”

IN the essay, Ofer Shelah, a veteran commentator, said that he had followed Mr. Mofaz for nearly 35 years. “Mofaz is a focused man in a way that is almost superhuman,” he wrote, adding that the new opposition leader had learned that “there is always an opening, if not through the door then through the window — a lesson he first learned when he failed three times to be accepted to the army’s officer training course.”

Mr. Mofaz plans to turn his modest background and unassuming assiduousness into assets at a time when many feel alienated from leaders like Defense Minister Ehud Barak, who recently sold an apartment for millions of dollars. Mr. Mofaz said that when social protests over high prices and indifferent government resume, as expected, this summer, he will be part of them because he understands the protesters.

“I have four children, two of them married, and three grandchildren,” he said. “My kids are among the young couples that can’t make ends meet. They work hard and can’t finish the month. In Israel of 2012, only part of the population enjoys the fruit of the country’s economic growth. The rich get richer and the poor poorer.”

Mr. Mofaz was born in Tehran and moved with his family to Israel at the age of 9, settling in the southern port of Eilat. His father had been a school principal in Iran, but his attempt to open a small factory in Eilat in the 1950s failed, and he was forced to seek work as a menial laborer. The family lived in one and a half rooms, two children to a bed, and there were days when the refrigerator was empty. At age 10, Mr. Mofaz worked in construction.

When he was 14, his father sent him to an agricultural boarding school in Nahalal, in the Jezreel Valley in northern Israel, a full day’s travel from home.

In an interview in 2009 with the newspaper Haaretz, Mr. Mofaz described what it was like for him there among the European elite.

“You’re in class with children from Nahalal who are Israelis with real roots in the country, children of the valley nobility,” he said. “These princes who live in the big houses on the big farms of Nahalal, and where do you come from? From nowhere, from Tehran, from Eilat, from a tiny apartment in a housing project.”

He rose at 4 a.m. to milk the cows, studied hard and realized that the short way to establishing roots here was through the paratroops, “because to serve in the paratroops and return to Nahalal on Friday with a red beret is to be Israeli.” Ultimately, he became chief of staff.

MR. MOFAZ’S security credentials, along with his tale of overcoming adversity as an Israeli of Middle Eastern origin, could offer powerful political advantages in a field of prospective leaders that includes a television host and journalist, Yair Lapid, who is expected to start a new party, and a former journalist and social activist, Shelly Yacimovich, the leader of the Labor Party. Both are members of the European Tel Aviv establishment.

It will depend on his ability to connect with the voters. His belief that Israelis want to talk about peace with the Palestinians seems counterintuitive. The issue has been fading from the public agenda, with most expressing the belief that Israel has no partner. But Mr. Mofaz says he would start with an interim Palestinian state on 60 percent of the West Bank and negotiate the rest.

Mr. Mofaz says Israel should keep the West Bank settlement blocs but give the Palestinians 100 percent of their territorial demands by swapping land. He believes that borders and security can be negotiated in a year, and that tens of thousands of settlers would leave their homes with the proper incentives. Those who remain would be forced out.

Then, he said, Israel could devote the resources used in settlements to its socioeconomic needs.

Yohanan Plesner, a Kadima legislator who began working closely with Mr. Mofaz 18 months ago, said it was not far-fetched to beat Mr. Netanyahu.

“Our polls show that we only have to capture 4 percent of the soft right to block Netanyahu’s hold,” he said. “With his security credentials and focus on rebuilding relations with the United States, Mofaz can do that. He may not have charisma, but he knows how to set a goal and build a team.”