World leaders have hailed Mr Obama's re-election. France, China, Russia, Australia and Britain, among others, have pledged to deepen their co-operation with America.
Russian President Vladimir Putin congratulated Mr Obama on his victory over Republican challenger Mitt Romney.
"We hope that the positive beginnings that have taken hold in Russian-US relations on the world arena will grow in the interests of international security and stability," Russian news agencies quoted a spokesman for Mr Putin as saying.
Moscow was ready to "go as far as the US administration is willing to go," Foreign Minister Sergei Lavrov was quoted as saying by the RIA Novosti news agency.
President Hu Jintao of China noted "positive progress" in Sino-US relations over the past four years despite tensions over issues such as trade and territorial disputes involving US allies.
China will "look to the future and make continuous efforts for fresh and greater progress in the building of the China-US cooperative partnership," a foreign ministry spokesman said.
Israeli Prime Minister Benjamin Netanyahu also joined the well wishers:
"I will continue to work with President Obama to ensure the vital security interests of Israel and the United States," said Mr Netanyahu.
British Prime Minister David Cameron said he was looking forward to working again with his "friend" Obama on several fronts, including helping the world economy and finding a solution for the escalating Syria conflict.
"There are so many things that we need to do: We need to kickstart the world economy and I want to see an EU-US trade deal," Mr Cameron said.
United Nations leader Ban Ki-moon urged Mr Obama to act quickly on ending the war in Syria and reviving the Middle East peace process.
German Chancellor Angela Merkel said she looked forward to continuing cooperation "so both our countries can continue to stand side-by-side to contend with the important foreign policy and economic challenges that we face as friends and allies".
AFP reports her message was echoed by European Union President Herman Van Rompuy, Commission President Jose Manuel Barroso and French President Francois Hollande.
Turkish President Abdullah Gul said the bonds between Turkey and the United States were strengthened during Obama's first term.