peace and of America's readiness to lead once more.
After a parade through Washington, Mr Obama and his wife Michelle attended official balls around the city on Tuesday evening, dancing before delighted guests.
Stars such as Rihanna, Mary J Blige and Queen Latifah were billed to perform at various venues.
Correspondents say the whole capital seems to have been partying with at least a dozen unofficial balls.
Outside America, Antigua announced it would rename its highest peak after Mr Obama while a village in the Irish Republic with ancestral links to the mixed-race new president was turning out commemorative cakes.
Mr Obama has set himself no less a task than to rebuild America, the BBC's Jane O'Brien reports from Washington.
The challenges facing Barack Obama in his first 100 days
He has already made history by becoming the first African-American president and how he will shape history is the next test, she says.
The US Senate, which traditionally moves swiftly to affirm a new president's cabinet, approved six members on Tuesday, including Janet Napolitano as homeland security secretary and Steven Chu as energy secretary.
However, Hillary Clinton's approval as secretary of state was postponed after a Republican senator demanded a debate beforehand about foreign donations to a foundation headed by her husband, former President Bill Clinton.
That debate is due on Wednesday and Mrs Clinton's nomination is now expected to be confirmed in a vote immediately afterwards.
Tim Geithner (right) faces Senate questions over his taxes
Timothy Geithner, the nominee to head the treasury department, is due to face the Senate finance committee on Wednesday to explain his initial failure to pay payroll taxes he owed while working for the International Monetary Fund.
Mr Obama last week called Mr Geithner's tax problems an embarrassment but an "innocent mistake".
Other Obama nominees still to be confirmed are Eric Holder as attorney general, and Tom Daschle as head of health and human services.
Night of celebration
One of the functions attended by America's new First Couple was billed as a "Neighbourhood Ball".
"We got the idea for the Neighbourhood Ball because we are neighbourhood people and I cut my teeth doing neighbourhood work," the president told guests.
"The word 'neighbourhood'... starts with 'neighbour' because it indicates a sense that we as Americans are bound together."
There were black-tie balls in Europe while in Mr Obama's ancestral Kenya, bulls and goats were slaughtered for feasts.
Alex Andrade, 24, an unemployed black Brazilian living in the Cantaglo slum of Rio de Janeiro, expressed some of the new US president's appeal to the wider world.
"Blacks face so much discrimination here," he told the Associated Press.
"Now with a black man in charge of such an important country, it might help decrease the racism in Brazil."
The Irish village of Moneygall decked itself in red, white and blue bunting in honour of a man whose great-great-great grandfather, local man Falmouth Kearney, had emigrated to the US in 1850 to escape the Great Famine.
Its commemorative brack, or fruit loaf, had a picture of Mr Obama on the wrapping.
In Antigua, Prime Minister Baldwin Spencer said that the 1,300ft (400m) Boggy Peak, the Caribbean nation's highest point, would be renamed Mount Obama on 4 August to mark the president's 48th birthday, AP reports.
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