Sharp differences remained between the US and Israeli positions on key issues Wednesday following Foreign Minister Avigdor Lieberman's first meeting with Secretary of State Hillary Clinton in Washington. While Clinton reiterated the American position that settlement expansion must stop, Lieberman indicated Israel had no intention of halting construction to accommodate natural growth. "We cannot accept this vision absolutely, completely freezing these settlements. I think we must keep natural growth," he said, at a joint press conference the two held at the State Department following their meeting. Watch the Lieberman-Clinton press conference When asked whether the US and Israel might be formulating some compromise on the issue, Clinton did appear, however, to leave room for such a possibility. "We believe that this process, which [special envoy] Senator [George] Mitchell is quarterbacking, for us has just begun. There are a number of critical concerns, many of which overlap in their impact and in their significance that will be explored in coming weeks," she said. At the same time, she disagreed strongly with the notion that the Bush administration had reached agreements with Israel that allowed for continuing some construction. Lieberman had alluded to these arrangements when he said: "We had some understandings with the previous administration, and we tried to keep this direction." Clinton, for her part, said: "Looking at the history of the Bush administration, there were no informal or oral enforceable agreements," saying that position had been "verified" by accounts from former Bush administration officials. She pointed specifically to a recent opinion piece by former US ambassador to Israel Daniel Kurtzer, who served under Bush but backed President Barack Obama in last year's election. Kurtzer wrote in Sunday's Washington Post that there were no understandings on settlement growth between the US and Israel. Israeli officials have said in recent weeks that there were tacit understandings with the Bush administration regarding where Israel could build in the settlements. This position was backed up by former deputy national security adviser Elliott Abrams, as well as Dov Weisglass, Ariel Sharon's former chief-of-staff. "We want to see a stop to the settlements," Clinton said. "We think it's an important and essential part of pursuing the efforts leading to a comprehensive peace agreement and the creation of a Palestinian state and an Israeli Jewish state that is secure." Clinton also stressed that the US remains committed to its policy of engagement with Iran, despite the demonstrations there and confusion over the outcome of the recent election. She said: "Obviously we intend to pursue engagement because we think it's in the interest of the United States and the world." "Our interest is to probe whatever opportunities might exist in the future," she continued, referring specifically to resolving issues over Iran's nuclear program and its support of terrorism. She also affirmed American's belief in the importance of freedom of expression in Iran and elsewhere. Israel has expressed reservations about the engagement strategy, though Lieberman said Wednesday that when it comes to dealing with Iran now, the issue is one of policy rather than personalities. Earlier in her comments, she referred to what she considered another fundamental American position, US support for Israel. "Our commitment to Israel's security is and will remain a cornerstone of our foreign policy," she said. In that vein, she referred to the importance of continuing the strategic dialogue between the US and Israel, a program that had been suspended because of elections in each country. Some time after Wednesday's meeting, Clinton fractured her right elbow during a fall. She was treated at The George Washington University Hospital, just a few blocks from State Department headquarters, before going home. She will undergo surgery to repair her elbow in the coming week, Mills said. Meanwhile, Israeli ambassador-designate to the US Michael Oren told Israel Radio Wednesday that there had been some progress on the settlement issue in recent days. "Both parties have expressed their determined will to put an end to this bone of contention, and some novel ideas have been proposed," he said, without elaborating on those ideas. Kurtzer, in his article, said Israel maintained that draft understandings discussed in 2003 between Sharon and US deputy national security adviser Stephen Hadley, as well as President George W. Bush's April 14, 2004, letter to Ariel Sharon, and a letter from Weisglass to National Security Adviser Condoleezza Rice constituted a "formal understanding in which the United States accepted continuing Israeli building within the 'construction line' of settlements." But, he argued, there was no such understanding. Kurtzer said that while the Bush administration did not regularly protest Israel's continuing settlement activity, silence did not mean consent. In a Jerusalem Post interview in September 2005, just before leaving office, Kurtzer said the US and Israel "tried very hard" after the April 14 letter to define the settlement construction issue, specifically whether there were "ways where we could find an area of agreement which would not mean the expansion of settlements, but would tolerate settlements within built-up areas." But, he said, "we never found enough common ground in defining what we were talking about to have the expert discussions, and we haven't had them." Asked what exactly the US meant when Washington said that there should be no settlement expansion, Kurtzer replied in 2005 that "there is still room for diplomatic discussion." He said that the issue was being discussed at the governmental level, "but to define it publicly, no." He would not say why there was such reluctance to define the issue publicly. Kurtzer's Washington Post piece differed with one written by Abrams, who indicated that though the understandings on the settlements were not formalized, they were understood. Abrams, who was a key player in the discussions on the matter between Israel and the US, wrote, "for the past five years, Israel's government has largely adhered to guidelines that were discussed with the United States but never formally adopted: that there would be no new settlements, no financial incentives for Israelis to move to settlements and no new construction except in already built-up areas. The clear purpose of the guidelines? To allow for settlement growth in ways that minimized the impact on Palestinians." Weisglass, who was also a key player in the discussions on the matter, wrote earlier this month in Yediot Aharonot that "there was no doubt" that when then Bush sent his letter to Sharon, "the administration recognized Israel's right under the road map to development from within the existing construction line in the Israeli settlements in Judea, Samaria and Gaza." AP contributed to this report.