Israeli PM Benjamin Netanyahu has arrived for talks at the White House with US President Barack Obama amid sharp differences on the way forward for the Middle East peace process.
Mr Obama has said a future Palestinian state must be based on the borders that existed prior to the 1967 war.
He said "mutually agreed swaps" would help create "a viable Palestine, and a secure Israel".
But Mr Netanyahu said the pre-1967 borders were "indefensible".
An estimated 500,000 Israelis live in settlements built in the West Bank, which lies outside those borders.
The settlements are illegal under international law, although Israel disputes this.
In a keynote speech on Thursday on the future of US policy in the Middle East, President Obama said: "The United States believes that negotiations should result in two states, with permanent Palestinian borders with Israel, Jordan, and Egypt, and permanent Israeli borders with Palestine.
"The borders of Israel and Palestine should be based on the 1967 lines with mutually agreed swaps, so that secure and recognised borders are established for both states."
In a statement, Mr Netanyahu's office said he appreciated Mr Obama's "commitment to peace" but that for peace to endure, "the viability of a Palestinian state cannot come at the expense of the viability of the one and only Jewish state".
The statement called on Mr Obama to reaffirm commitments made to Israel by the US in 2004.
"Among other things, those commitments relate to Israel not having to withdraw to the 1967 lines which are both indefensible and which would leave major Israeli population centres in Judea and Samaria beyond those lines," it said.
"Those commitments also ensure Israel's well-being as a Jewish state by making clear that Palestinian refugees will settle in a future Palestinian state rather than in Israel."
US officials told Associated Press a "passionate" Mr Netanyahu had tried to have the section about borders removed from Mr Obama's speech and was incensed when he failed.
One Israeli official travelling to Washington on the plane with Mr Netanyahu said: "There is a feeling that Washington does not understand the reality, doesn't understand what we face."
But Arab League chief, Amr Moussa, on Friday called on President Obama to remain committed to a Palestinian state based on the 1967 borders.
And the Middle East Peace Quartet - which combines the European Union, United Nations and Russia with the US - on Friday expressed "strong support" for President Obama's peace plan.
The BBC's Kim Ghattas in Washington says the "agreed swaps" phrase will have to be clarified, though the US will want the Israelis and Palestinians to negotiate this with each other - it is not a detail the US wants to get into at the moment.
She says Mr Obama may be attempting to give the Palestinians something they have long sought in order to convince them not to go to the UN in November and try to declare a Palestinian state unilaterally.
The BBC's Wyre Davies in Jerusalem says Mr Netanyahu is coming under increasing international pressure to ease his objections to such a state following the unity deal signed this month between rival Palestinian groups Hamas, which governs Gaza, and Fatah, which runs the West Bank.
Israel's claim to being the only democratic state in the region has also been undermined by the dramatic developments of the "Arab Spring" anti-government uprisings, our correspondent adds.
The push for democracy began with the overthrowing of Tunisian President Zine al-Abidine Ben Ali in January. Egyptian leader Hosni Mubarak was later toppled in Egypt, with demonstrators in Libya currently working to overthrow Muammar Gaddafi.
Similar uprisings are also taking hold in Bahrain, Yemen and Syria.
A senior member of Hamas, Foreign Minister Mohamed Awad, told the BBC that tangible steps were needed from the US president, not mere slogans.
"Obama didn't say anything about the suffering of the Palestinian people, who are suffering for more than 63 years," he said.
"He didn't say that the peace process had already reached a dead end... He tried to please everyone but he didn't try to please the Palestinian people."