On Monday morning, Yameen wrote three letters to the Supreme Court explaining the challenges being faced in implementing the court order.
Mr Nasheed was an opposition leader under a former government and became the country's first democratically elected leader in 2008, but was ousted and jailed in 2012. "President Yameen should resign immediately".
Meanwhile, former Maldivian President Mohamed Nasheed has asked India to send military help to stem the ongoing political crisis.
Another former President Mohammed Nasheed, who is now under exile, termed the emergency as unconstitutional and called upon people not to follow orders.
Observers say China faced a similar situation in Sri Lanka when its close ally and the then president Mahinda Rajapaksa was defeated in 2015 elections creating crisis situation for Chinese strategic investments.More news: Liverpool coach delivers verdict on new signing Tony Gallacher's under-23 debut
Soon after the emergency declaration on Monday evening, soldiers forced their way into the Supreme Court building, a spokesman for the court said on Twitter.
"President Yameen's announcement today - which declares a State of Emergency, the banning of fundamental freedoms, and the suspension of the Supreme Court - is tantamount to a declaration of martial law in the Maldives.
The government does not believe that the Supreme Court ruling to release the political prisoners can be enforced".
The opposition leader also urged the United States to stop Maldives government officials from making transactions through American banks.
President Abdulla Yameen declared the state of emergency on 5 Feb, having defied a shock ruling from the Supreme Court that quashed convictions ranging from terrorism to corruption and ordered the release of nine leading opposition figures, on grounds that the cases against them were politically tainted.More news: Two well-known Karnataka personalities join BJP
There was no immediate response from India or the United States, though both have called on Mr Yameen to obey the supreme court order.
In a video message shortly before his arrest, Gayoom said: "I have not done anything to be arrested".
The opposition and general public have been unrelentingly asking President Yameen to step down and allow a new leadership to take charge.
India on Tuesday said that it was disturbed by the situation in the Maldives where President Abdulla Yameen has declared a state of emergency.
He was granted medical leave in 2016 and travelled to Britain where he was granted asylum.More news: China opposes new United States nuclear strategy
Nasheed is among a total of nine individuals whom the apex court declared were subject to unfair judicial proceedings and therefore can not be kept in prison.