Israeli Prime Minister Ehud Olmert says he is ready to negotiate peace with the Palestinians but not until Hamas rejects violence and recognises Israel.
"I extend my hand in peace to Mahmoud Abbas, the elected president of the Palestinian Authority," Mr Olmert said in a keynote speech to the US Congress.
But Israel "will not give a terrorist regime a veto over progress or allow it to take hope hostage," he said.
Israel, the US and the EU consider Hamas a terrorist organisation.
Hamas, which dominates the PA, has refused to recognise Israel. It won elections in January and formed a government.
At talks on Tuesday, President George W Bush supported Mr Olmert's idea to redraw Israel's borders unilaterally if peace talks failed.
A Hamas spokesman said that would spell the end for the Palestinian cause.
There is concern in the US that Israel may go it alone - without at least consulting other countries, says the BBC's Jonathan Beale in Washington.
Mr Olmert's appeal to Mr Abbas was in stark contrast to his earlier criticism that the Palestinian leader was powerless and weak, says our correspondent.
Israel's prime minister appears to have heeded US calls for him to make an effort to engage with moderate Palestinians, he says.
Mr Olmert was addressing a joint session of US Congress - a rare honour reserved for close allies of the US.
Palestinians fear Israel's border plan may reduce their land
Israel, he said, was willing to negotiate peace with the PA - but it had to "renounce terrorism, dismantle terrorism infrastructure, recognise previous agreement and recognise the right of Israel to exist".
Mr Olmert repeated that Israel could not wait for the Palestinians forever.
"The Palestinian leadership that fulfils its commitments and obligations will find us a willing partner in peace.
"Should we realise that the bilateral track with the Palestinians is of no consequence, should the Palestinians ignore our outstretched hand for peace, Israel will seek other alternatives to promote our future, and the prospects of hope in the Middle East. At that juncture, the time for realignment will occur.
"We will move forward - but not alone," he said citing US support for Israel's unilateral disengagement from the Gaza Strip last year.
It now remains to be seen how much faith Mr Olmert has in the PA president and how far he is prepared to go - or whether he is simply going through the motions, our correspondent says.
Mr Olmert's plan envisages the withdrawal of tens of thousands of Israelis from isolated settlements in the West Bank while, at the same time, consolidating other settlements housing hundreds of thousands of others.
Palestinians see the Israeli plan as a land grab of territory captured by Israel in 1967 and have condemned it.