World leaders have congratulated US President George W Bush on the clear-cut election victory that will give him a second term in office.
Bush has not won hearts and minds in the Arab world
But many - including key allies - have warned
that the US faces major challenges in the Middle East.
Mr Bush won about 51% of the vote and at least 274 electoral college votes to beat John Kerry in Tuesday's poll.
Mr Kerry admitted defeat when it became clear that he would not win the key state of Ohio.
Mr Bush praised his opponent and said he was "proud to lead such an amazing country".
World leaders were quick to respond to the news of his victory - some in warmer terms than others.
British Prime Minister Tony Blair, a key ally, said: "The need to
revitalise the Middle East peace process is the single most pressing political challenge in our world today."
Egyptian President Hosni Mubarak cited the need for "peaceful development" in the region in his congratulations to Mr Bush, as did a spokesman for ailing Palestinian leader Yasser Arafat.
But BBC Arab affairs analyst Magdi Abdelhadi says Mr Bush's victory was greeted with general dismay in the Arab world, where anti-American feelings are running high in the wake of the US-led invasion of Iraq.
BBC world affairs editor John Simpson says Mr Bush's victory may in fact make life easier for countries such as France and Germany, which have had tense relations with him after strongly opposing the war in Iraq.
If Mr Kerry had got in they might have been forced to do something about helping with Iraq but now they do not need to, he says.
In his victory speech, Mr Bush made reference to Iraq as well as Afghanistan - the other country invaded and occupied by the US during his first term.
He said the US would "help the emerging democracies of Afghanistan and Iraq to grow in strength and freedom".
"And then our servicemen and women will come home with the honour they have earned," he added.
Mr Bush set out a conservative social and economic agenda for his second four-year term, singling out tax reform, social security and education as priorities.
President Bush will begin his new term in January with strengthened Republican majorities in both houses of Congress.
Projections put turnout in the presidential election at more than 115 million voters - 10 million more than in 2000.
The projected vote showed Mr Bush leading Mr Kerry nationwide by three-and-a-half million votes.