WASHINGTON — Hillary Rodham Clinton and Avigdor Lieberman last week reiterated their countries’ disagreement over settlements.

Clinton, the U.S. secretary of state said, however, that a number of “critical concerns” will be explored in upcoming talks with special U.S. Middle East envoy George Mitchell.

Speaking to reporters after the two met in Washington, the Israeli foreign minister said that “natural growth” of settlements “must” continue.

“We don’t have any intention to change the demographic balance in Judea and Samaria,” Lieberman said, using Israel’s terms for the West Bank.

But “every place around the world, babies are born and people get married. We can’t accept this vision about absolutely, completely freezing settlements.”

“We want to see a stop in settlements,” said Clinton, who has said in the past that “natural growth” is included in a settlement freeze. “We think that is an important and essential part of pursuing the efforts leading to a comprehensive peace agreement.”

Clinton also indicated, however, that there was more discussion on the issue to come.

“We believe that this process that Senator Mitchell is quarterbacking for us has just begun,” she said. “There are a number of critical concerns that will be explored in the coming weeks as Senator Mitchell engages more deeply in the specifics of where Israelis and Palestinians are willing to go together.”

Reuters has reported that Israeli and western officials are discussing with the Obama administration whether projects already underway in a settlement, or cases in which money spent on a project cannot be reimbursed, could continue.

In a June 17 meeting with reporters, the two top diplomats also disagreed about the validity of understandings that Israel says it reached with the Bush administration to allow some natural growth in certain settlements.

While Lieberman said Israel wanted to “keep” those understandings intact, Clinton said there were “no informal or oral enforceable agreements” on the issue, and “that has been verified by the official record of the Bush administration and personnel in positions of responsibility.”

She also noted a recent Washington Post op-ed by Dan Kurtzer, the U.S. ambassador to Israel at the time, stating that “no such understanding” was ever reached on settlements, as reflecting the administration’s position. Kurtzer also was a supporter of and surrogate for Barack Obama in the Jewish community during the presidential campaign.

In related developments, Mitchell said the United States continues to demand that Israel halt the “natural growth” of settlements.

In a press briefing last week at the State Department, he called “highly inaccurate” an Israeli newspaper report claiming that the Obama administration would allow “natural growth” of settlements and emphasized there has been “no change in our policy.”

But when asked for a definition of the term “natural growth,” Mitchell was unclear, first saying there was no accepted definition, then stating that “the most common definition” is “number of births.”

“Well, of course, one of the issues is that there is no universally used and accepted definition,” he said, according to a transcript. “The most common definition is by the number of births, but there are many variations of that. I’ve had numerous discussions with many Israeli and other officials, and there are almost as many definitions as there are people speaking. But I think the most commonly used measure is the number of births.”

Asked a follow-up question, Mitchell declined to elaborate further.

Mitchell also said he hoped that negotiations between Israel and the Palestinians could resume in “a matter of weeks, not many months.”