Re-elected US President Barack Obama today told ecstatic supporters the "best is yet to come" in a victory speech in his home city of Chicago.

Flanked by wife Michelle and daughters Malia And Sasha, the jubilant Democrat congratulated opponent Mitt Romney on a "hard fought campaign" and revealed he would work with the former Massachusetts governor to take the country forward.

President Obama vowed to revive America's economy but warned "progress will come in fits and starts".

Although exit polls put the two candidates neck and neck, Obama secured a convincing victory. Under the electoral college system, which allots votes to states according to population size, he has 303 while Romney is on 206, with Florida yet to declare.

Rival Mitt Romney earlier conceded defeat, phoning the President to congratulate him on his victory.

He told his supporters he and running mate Paul Ryan had "given our all" to the campaign and said he wished his Democrat opponent well.

The millionaire Mormon businessman urged his supporters to pray for the re-elected President as he returns to the White House against a backdrop of economic gloom.

He added: "I so wish that I had been able to fulfil your hopes to lead the country in a different direction but the nation chose another leader and so I join with you to earnestly pray for him and for this great nation."

At his headquarters in Boston, Massachusetts, Romney addressed a ballroom full of the Republican party faithful to thank them for their support.

He told them: "Thank you my friends, thank you so very much. I have just called President Obama to congratulate him on his victory. His supporters and his campaign also deserve congratulations.

"I wish all of them well, but particularly the president, the first lady and their daughters.

"This is a time of great challenges for America, and I pray that the president will be successful in guiding our nation."

Today David Cameron sent his congratulations to Barack Obama, saying: "I think he's a very successful US President and I look forward to working with him in the future."

Speaking during a tour of the Middle East, the Prime Minister said: "I would like to congratulate Barack Obama on his re-election.

"I have really enjoyed working with him over the last few years and I look forward to working with him again over the next four years.

"There are so many things that we need to do: we need to kick start the world economy and I want to see an EU-US trade deal.

"Right here in Jordan I am hearing appalling stories about what has happened inside Syria so one of the first things I want to talk to Barack about is how we must do more to try and solve this crisis."

The results of yesterday's election were closely watched in many countries. Several US embassies held mock elections and threw parties as returns came in.

China's Foreign Ministry said President Hu Jintao and Premier Wen Jiaobao phoned Obama to congratulate him. Vice President Xi Jinping, who is to begin taking over this week in China's once-a-decade leadership transition, phoned Vice President Joe Biden to congratulate him.

Russian President Vladimir Putin's welcomed Obama's re-election and hoped it will have a positive impact on ties with the United States.

Russian Foreign Minister Sergei Lavrov also said Moscow was ready to take cooperation with the US government as far as Washington was willing to go.

Israeli prime minister Benjamin Netanyahu, who has had a strained relationship with the American President over his policies on Iran and the Israeli- Palestinian conflict, congratulated Obama in a text message.

"I will continue to work with President Obama to preserve the strategic interests of Israel's citizens," he said.

In China, Obama's re-election was good news for people concerned about Romney's vow to label the country a currency manipulator if elected. Some feared that would ignite a trade war between the world's two biggest economies.

"His re-election is in line with what the Chinese people want," said Hong Zihan, a graduate student who monitored the results at a US Embassy event in Beijing.

Washington has started focusing more on Asia since Obama took office. Some Asian countries, including the Philippines and Vietnam, have been looking more toward the US as tensions flare with China over disputed territories in the South China Sea.

A spokesman for the main Syrian opposition bloc, the Syrian National Council, expressed hope that the election victory would free Obama to do more to support those trying to oust Syrian president Bashar Assad.