The United States and the African Union have dropped their demands that last week's coup in Mauritania be reversed.
Mauritania's new rulers have pledged to stand aside peacefully
The US is now working with the military junta to ensure that multi-party elections are held as soon as possible, a State Department spokesman said.
President Maaouiya Ould Sid Ahmed Taya was criticised at home for working with the US in trying to fight alleged terror groups in the Sahara desert.
AU officials called the junta leader "president" after meeting him.
AU delegation leader Nigeria's Foreign Minister Oluyemi Adeniji stressed that elections should be held soon, and did not call for Mr Taya to be brought back.
"All the people we met with indicated they agreed with the change - we think it would be simpler to take the transitional process toward democracy," he said.
He, however, said that Mauritania would remain suspended from the AU until elections are held.
Meanwhile, a new government has been appointed.
None of Mr Taya's ministers have been retained but Ahmed Ould Sid'Ahmed, the foreign minister who signed the 1999 deal establishing diplomatic relations with Israel, has been given his old job back.
The head of the military council, Colonel Ely Ould Mohamed Vall, looks set to take on the duties of defence minister, after no-one else was named to this post.
The military council has pledged to hold elections within two years and to forbid any member of the military junta from standing for office in that contest.
US State Department spokesman Adam Ereli said the US was working with the junta on that basis.
"The guys running the country right now are the guys we're dealing with, because they're the ones making the decisions and we are trying to get them to make the right decision," he said.
The BBC's Pascale Harter in Mauritania says the coup has initially proved popular with Mauritanians, many of whom were exasperated by two decades of repression under Mr Taya.
Thousands of people flocked into the streets when news of the coup emerged last week.
Within hours all the country's opposition parties backed the new rulers, with Mr Taya's own party, the Social Democratic Republican Party (PRDS), also throwing its weight behind the junta.
But Mr Taya is vowing to return and has gone to The Gambia from Niger.
"As the president of the republic, I order officers, non-commissioned officers and soldiers of the armed forces and security forces to put an end to this criminal operation in order to restore the situation to normal," he told Al-Arabiya television on Monday.