A statement from the President's office said the three envoys would visit "friendly nations ... and provide updates on the current situation".
The envoys have already reached China and Pakistan, it said.
The announcement came after China, with apparent reference to India, on Wednesday cautioned against outside interference in the Maldivian affairs, saying it would "complicate" the situation.
New Delhi received multiple appeals from the country's exiled former President Mohamed Nasheed in the last few days to intervene to resolve the deepening political crisis.
He said on Wednesday that his countrymen viewed New Delhi's role "positively" during the 1988 crisis when India were "not occupiers but liberators". Indian troops then sailed into the Maldives and saved then President Maumoon Gayoom from being toppled.
India has now said it was "disturbed" by the situation in the Maldives.