By Jill McGivering
BBC State Department correspondent
Washington is hailing the new Palestinian president with cautious optimism.
US President George W Bush was quick to congratulate Mahmoud Abbas publicly and has already extended a general invitation to the White House.
His gesture mirrors hopes that Israeli Prime Minister Ariel Sharon might also agree to meet the new Palestinian president in the coming days.
All this is in marked contrast to their refusal to deal with Yasser Arafat - and is feeding heightened expectations about a fresh start.
Abbas will have to prove he is different from predecessor Arafat
Yasser Arafat's death was hailed almost at once by the US as "an opportunity".
He was repeatedly accused of being the main obstacle to progress in the peace process, vilified by the US as corrupt and untrustworthy, a figure with whom they simply could not do business.
Some might argue he had also become a convenient whipping boy for the failures in advancing the grand US design, the roadmap.
Now those days are over. But with the new hopes come new uncertainties about how far Mahmoud Abbas can deliver in the key areas which will determine whether the peace process can be rekindled - or continue to falter.
The US friendliness is highly conditional.
The administration stands squarely with Israel in expecting visible and substantial progress on the security front before negotiations can continue.
Mr Abbas faces demands to consolidate control of the security forces and show he is serious about curbing militancy.
Burden on Mr Abbas
Some right-wing US voices are already expressing scepticism about his intentions, complaining that he has not yet gone far enough in renouncing militancy on a permanent basis.
Others recognise what a difficult line Mr Abbas is walking, trying to show willingness in the face of US and Israeli demands without further deepening divisions with powerful groups like Hamas.
Mr Abbas will also be under pressure to make quick visible progress on reforming Palestinian institutions, in the face of long-standing allegations of rampant corruption.
The US seems ready to offer concrete incentives in the form of increased aid.
The message from Washington seems to be that significant help will be forthcoming - but the onus is on the new president to demonstrate change first.
Increased practical support from Washington could prove crucial as the Palestinian
Authority prepares to fill the vacuum soon to be created by the Israeli withdrawal from Gaza.
An improved atmosphere and new momentum returning to the peace process could ease that sensitive transition significantly.
Key to Mid-East peace
The sceptics point out that these and other fundamental areas of contention between the Israelis and the Palestinians, which have stymied the peace process so far, have not gone away, even with a new president.
But the opportunity of the new presidency is combined with fresh US determination to throw its full diplomatic weight behind restarting the peace process in the administration's second term.
In the meantime, there is a sense of waiting - waiting for outgoing Secretary of State Colin Powell to leave office and be replaced by Condoleezza Rice.
There is already speculation she may make a visit to the region as soon as March.
Her closeness to President Bush could help her to play a key role, both in urging the new presidency to make the moves that Israel and the US demand - and in putting pressure on the Israelis to respond positively when they do.
Progress in the Israel-Palestinian conflict is central to President Bush's personal vision of peace and spreading democracy in the Middle East.
That goal was compromised in the first term. He seems determined to get it back on track in the second - and waiting, too, to see how far Mahmoud Abbas can realise the fresh hopes.
His real challenge was not on Sunday - there was little doubt about his election victory - but in the crucial next phase, as his mettle and policies as president are put to the test.