Prime Minister Benjamin Netanyahu would be willing to withdraw from most of the West Bank and evacuate numerous settlements as part of an agreement with the Palestinians, as long as his security demands were satisfied, a senior cabinet minister from Netanyahu's Likud party told Haaretz on Wednesday.

The senior minister, who requested anonymity due to the sensitivity of the issue, said Netanyahu knows very well that if negotiations with the Palestinians resume under U.S. Secretary of State John Kerry's auspices, he will have to hold serious discussions on the borders of a Palestinian state.

"Netanyahu understands that for a peace agreement, it will be necessary to withdraw from more than 90 percent of the West Bank and evacuate more than a few settlements," he said. "He knows this is one of the things that will be discussed."

The minister said the issue of security arrangements is Netanyahu's main concern, and this will be his main demand in the negotiations. If his security demands are met, he is prepared to make significant territorial concessions, the minister added.

Inter alia, Netanyahu wants the future Palestinian state to be demilitarized, and he also wants the Israel Defense Forces to be able to maintain a long-term presence along the Jordan River, even if Israel cedes sovereignty there.

Another Israeli source who is familiar with the discussions Netanyahu has been holding on the Palestinian issue said much the same thing as the senior minister.

"Netanyahu doesn't have a map of the borders of the future Palestinian state," this source said. "But all of his considerations on this issue stem from practical issues, not from ideology. His two key principles are maintaining the settlement blocs as part of Israel and a military presence in the Jordan Valley, without Israeli sovereignty there."

The senior minister said that Netanyahu very much wants to resume talks with the Palestinians, but the premier isn't convinced that Palestinian Authority President Mahmoud Abbas is equally eager. "He's not certain there's a partner," the minister said.

He also said Netanyahu believes the talks will have to continue for at least a year, and that he's interested in serious negotiations, not the kind that will blow up after a few weeks. "At first, everyone will take extreme, hard-line positions," he said. "But Netanyahu thinks these positions will start to coalesce once both sides begin to see the entire package."

Despite appearances to the contrary, the minister continued, Netanyahu would be able to mobilize broad-based political support for a deal with the Palestinians, even within Likud. "If he leads it, they'll go with him," he said. "Even those who today present themselves as right-wing."

He said Netanyahu won't have any political problem in terms of maintaining his government, since he can either form a coalition with the Labor Party or get it to support him from outside.

"Netanyahu understands the situation," the minister said. "You hear this in what he says, and also in how he says it. He believes that an agreement on two states for two peoples would be good for the country."

The Likud minister's statements echo those made last week by the heads of Netanyahu's two biggest coalition partners, Economy Minister Naftali Bennett (Habayit Hayehudi ) and Finance Minister Yair Lapid (Yesh Atid ). In separate interviews with the Washington Post, both said Netanyahu seriously wants to advance the peace process.

Most settler leaders think this as well. When Netanyahu visited the settlement of Barkan on Monday, Gershon Mesika, the head of the Samaria Regional Council, sounded like he did before the disengagement from Gaza in 2005. "Don't give in to pressure from within or without," Mesika urged Netanyahu. "Peace doesn't mean throwing children out of their homes."

Many on the right believe that Netanyahu intends to turn his back on the settlers, and perhaps even on his own party, in order to advance a historic deal with the Palestinians. Netanyahu's repeated statements about his fear that Israel will become a binational state have only strengthened this belief.

"For me, this lit a red light, because that's the terminology of a leftist," said a senior figure on the Yesha Council of settlements, who asked to remain anonymous.

Kerry will arrive in Israel on Thursday for a fifth round of talks in his ongoing effort to restart Israeli-Palestinian negotiations. He will meet with Netanyahu in Jerusalem Thursday night, and with Abbas in Jordan Friday. On Saturday night, he will return to Jerusalem to meet with Netanyahu again.

At this stage, there are no signs that Kerry is nearing a breakthrough that would enable direct Israeli-Palestinian talks to resume. At a press conference in Kuwait on Wednesday, he stressed that he isn't setting a deadline for his efforts. But for the first time, he did set a target date: He would like to see progress before the United Nations General Assembly convenes in September.

"Time is the enemy of a peace process," Kerry said. "Time allows situations on the ground to change and/or to harden, or to be misinterpreted. The passage of time allows a vacuum to be filled by people who don't want things to happen."

Therefore, he continued, "long before September, we need to be showing some kind of progress in some way, because I don't think we have the luxury of that kind of time."

Abbas has recently said he was willing to give Kerry until September, and senior administration officials told the Associated Press that the White House is also willing to give him until September.

Knesset Foreign Affairs and Defense Committee chairman Avigdor Lieberman, whose Yisrael Beiteinu party ran a joint slate with Likud in the last election, charged Wednesday that Abbas doesn't actually want to resume negotiations, but does want to engage in some "maneuver of incitement and provocation" at the United Nations in September, and to do so, he knows he must "make it look as if he wants peace, so that he'll ultimately be able to blame Israel."