Mohamed Nasheed, the country's exiled former president, urged neighbouring India on Tuesday to send "an envoy, backed by its military" to free two Supreme Court judges and a former president who were arrested in the capital Male after the emergency declaration.
"We are asking for a physical presence," Nasheed said in his appeal.
He also urged the United States to impose targeted sanctions on Yameen and his associates.
The Maldives, an Indian Ocean archipelago, was plunged into turmoil on February 1 when its Supreme Court issued a shock ruling that overturned terrorism convictions against nine of Yameen's opponents, including Nasheed, and ordered those in jail be freed.
In a televised address on Tuesday, the president said he declared a state of emergency to investigate a "coup" against him.
Accusing Chief Justice Abdulla Saeed and Judge Ali Hameed of corruption and judicial overreach, Yameen said the bench had deliberated on removing him and his attorney general, and discussed reinstating two police chiefs he had sacked over the weekend.
"I had to declare a state of emergency because I had no way to hold a judge of the Supreme Court accountable," he said. "I had to suspend [their immunity] to find out how thick this plot, this coup was."
|Yameen said he declared an emergency to investigate a coup against him [Handout/ Al Jazeera]|
The emergency decree gave security forces sweeping powers to make arrests and curtailed the authority of the judiciary.
Shortly after the emergency was announced on Monday, security forces stormed the Supreme Court building and arrested Saeed and Hameed. The remaining three judges on the top court bench were not detained.
Yameen's estranged half-brother, former President Maumoon Abdul Gayoom, who has sided with the opposition, was also detained in the early hours of Tuesday.
Police also took Mohamed Nazim, a former defence minister who was under house imprisonment, into custody on Tuesday. Nazim was sentenced to 11-years in jail on weapons smuggling charges in 2015, and was among the nine whose release the top court had ordered last week.
Meanwhile, the parliament, where the opposition have a majority, remained suspended.
In his appeal on Tuesday, Nasheed, the former president, accused Yameen of declaring "martial law" in the Maldives.
"We must remove him from power," he said.
"We would also like the US government to ensure that US financial institutions stop all US$ financial transactions of the regime leaders in the Maldives," he added.
There was no immediate reaction from the US and India to Nasheed's appeal.
India's Ministry of External Affairs, in a statement on Tuesday, said it was "disturbed" by the state of emergency in the Maldives
The US meanwhile called for restraint.
"The Maldivian government and military must respect the rule of law, freedom of expression, and democratic institutions. The world is watching," the US National Security Council said in a Twitter post on Monday.
The UN, EU and UK have urged Yameen to revoke the emergency.
China, India, Australia and the US have issued travel advisories for the Maldives.