Waheed, who was Nasheed's vice president, was swiftly sworn in as the new head of state following the resignation announcement. [UPDATE: Ex-Prez Nasheed missing; Arrest warrant issued]
In a public statement posted on the presidential website, he indicated that Nasheed's decision to step down was the direct result of popular public pressure following three weeks of anti-government protests.
"The nation witnessed difficult times in the recent past, but today the Maldivian people have made a momentous decision," Waheed said.
"Following that decision ... at any cost, the rule of law must be upheld," he added.
He made no direct mention of the mutiny in police ranks today which saw officers side with the protesters and was seen as a major factor in forcing Nasheed's resignation.
However, with Nasheed's aides and supporters alleging that the president had been ousted in what amounted to a coup, Waheed gave assurances that "no unlawful order" would be issued to the police or the military.
Stressing the need for political differences to be put aside, Waheed also warned that "no law must be violated in any revenge against the past political leaders," the statement said.