"The complaint has been made to the defence ministry, but we have also taken note of it and begun our own investigations," police spokesman Abdulla Nawaz told AFP by telephone. "We take this seriously."
He said Nasheed, 46, was currently being accorded protection by the Maldivian National Defence Force (MNDF).
Nasheed's office said in a statement that they had information about an assassination plan involving two Al-Qaeda operatives who had already arrived in the capital Male.
Nasheed, a former president who was toppled 20 months ago, had won the first round of elections on September 7 with 45 per cent of the popular vote, which should have led to a second-round run-off.
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However, the country's highest court annulled those results and called fresh elections which were due to open on October 19, but police stopped that vote going ahead citing disputed procedural flaws.
If no candidate gets 50 per cent at the rescheduled polls on November 9, a runoff is due on November 16. Candidates could still scuttle the election by refusing to endorse the voter list which happened on October 19.