The new government denies the coup claims and insists Nasheed stepped down voluntarily. It has made no move to arrest Nasheed, who is living openly in his home in Male, the capital.
Hassan has announced his intention to form a coalition to help restore stability ahead of fresh presidential elections due next year.
However, Nasheed is calling for early elections, insisting his party would emerge victorious.
The United States initially recognized the new Maldives government on Friday. It later backtracked, saying the situation was unclear.
Male remained peaceful Saturday. There were no signs of extra security on the streets and people went about their normal lives.
Tourism is the main industry in the Maldives, a chain of nearly 1,200 islands off southern India blessed with sandy beaches and coral.