ABC News' Kirit Radia reports: The US has ratcheted up the rhetoric in recent weeks, demanding that Israel halt settlement construction in the West Bank, including so-called "natural growth" of existing sites, but it doesn't seem to have made a difference to the new right-wing Israeli government. Prime Minister Netanyahu said in a major policy speech Sunday that Israel maintains the right to the natural expansion of settlements, essentially rejecting the US calls for a building freeze. Today, the difference of opinion was on full display when Secretary of State Hillary Clinton met with her Israeli counterpart, the nationalistic Foreign Minister Avigdor Lieberman who himself lives in a settlement community. "We really don't have any intention to change the demographic balance in Judea and Samaria," Lieberman said. "We cannot accept this vision about absolutely, completely freezing of settlements. I think that we must keep the natural growth." Clinton didn't flinch, saying: "We want to see a stop to the settlements. We think that is an important and essential part of pursuing the efforts leading to a comprehensive peace agreement and the creation of a Palestinian state next to a Israeli Jewish state that is secure in its borders and future." The clash has led to some rare tension in the US-Israeli relationship, and was amplified over Israeli anger that the Obama administration does not recognize, or even acknowledge the existence of, what Israel says was a handshake agreement with the Bush administration to allow settlement activity to continue. "We have some understandings with the previous administration, and we tried to keep this direction," Lieberman said today. "In looking at the history of the Bush administration, there were no informal or oral enforceable agreements. That has been verified by the official record of the administration and by the personnel in the positions of responsibility," Clinton said in response. Dov Weisglass, former Chief of Staff to then-Prime Minister Ariel Sharon, wrote in an op-ed on June 2 that President Bush wrote a letter to Sharon in 2004 that recognized Israel's right to settlement construction. Not to be outdone, Daniel Kurtzer, the US Ambassador to Israel at the time, wrote his own op-ed in the Washington Post on Sunday disputing that account. Kurtzer said agreements were never codified and would have only allowed for settlement growth within a specified perimeter. "Throughout this period, the Bush administration did not regularly protest Israel's continuing settlement activity. But this is very different from arguing that the United States agreed with it," Kurtzer wrote. Still, some sort of deal may be afoot. Michael Oren, the incoming Israeli ambassador to Washington, said yesterday that there could be some compromise in the works. "I think there is flexibility on both sides. and I'm confident that we can work this out. I think that both the Obama administration and Israel want to move forward on the peace process. We don't want to get caught up in this issue," Oren told The Associated Press. An Israeli official told ABC News today that talks are ongoing that could lead to a compromise on settlements. Yesterday US Special Envoy for Middle East Peace George Mitchell told reporters that unspecified reports that the US could allow natural growth of settlements "highly inaccurate." Mitchell refused, however, to be pinned down on a definition of natural growth. He will travel to Paris next week to meet with Israeli Prime Minister Netanyahu, their second meeting in three weeks. In his speech on Sunday, Netanyahu for the first time endorsed the notion of a Palestinian state living alongside Israel, but he placed a number of conditions for Israel to allow that to happen, including that such a state be demilitarized, that will be nonstarters for the Palestinian side. Asked how progress can be made in such an atmosphere, Clinton reached back into the history books to say past Israeli leaders have changed their positions to accommodate negotiations. "I personally have known such prime ministers, from Labor, Likud and Kadima, who started in one place but, in the process of evaluating what was in the best interest of Israel … have moved to positions that they never would have thought they could have advocated before they started looking hard and thinking hard about what the future should be," she said. "I leave that to them to decide. I'm just reflecting on history and on people who've been in these positions over the last 30, 40 years," Clinton replied when asked if this was a subtle message to Netanyahu and Lieberman.