An official statement by the Maldives Embassy on Friday said that the first stop of the special envoy had actually been planned for India but had to be cancelled due on the request of the Indian government, citing unavailability of dates.
Yameen was elected as President in 2013, defeating Maldivian Democratic Party (MDP) leader and former president Mohamed Nasheed in the 2013 elections.
On the political crisis, India has strongly reacted saying that it has "disturbed" on the declaration of an emergency by the government there and described the arrests of Supreme Court Chief Justice and political figures as a matter of concern.
Yameen has cracked down on civil liberties since coming to power in 2013, imprisoning or forcing into exile almost every political leader who opposes him.
Nasheed told reporters in the neighboring country of Sri Lanka that current President Yameen Abdul Gayoom has opened the doors to Chinese investment without regard for procedure or transparency. Sources on condition of anonymity said most countries are looking to India to take a lead in dealing with the problems in Maldives given its proximity and ability to influence events in the archipelago.
The UK Foreign Office has been advising British visitors to "exercise caution" and to avoid any protests or rallies since a state of emergency was imposed in the capital Male on Monday.
Tourism dominates the country's economy, with wealthy foreigners who stay at hyper-expensive resort islands.
Over the past few days, global voices calling for Yameen to return to some sort of democratic rule are increasing despite China, Yameen's primary backer, calling for dialogue between political parties in Maldives.
As a small country in South Asia and the Indian Ocean, Maldives has neither big strategic expectations, nor can it become a strategic pivot of China in the region.
Almost 1.4 million people visited the Indian Ocean island nation past year and nearly a third were from China. The others are Pakistan and Saudi Arabia.
Although the Yameen government is friendly to China, it's not anti-India.
The country's foreign ministry said in a statement Wednesday that the invitation was being offered so critics can assess the situation in the country and its level of safety and security.
Kondapalli said the sending of special envoys to China, Pakistan and Saudi Arabia suggested Yameen was desperate to "cling on to power".
"We await the convenience" of the government of India, he added.
The island nation is now under a state of emergency, which gives the security forces sweeping powers to arrest people.
Mr Saeed's lawyer claimed that his client received death threats before his arrest.
The ' chief justice is being unconstitutionally detained after being forcefully dragged on the floor from his chambers by security personnel in riot gear, his lawyer said Thursday, expressing grave concern about the reaction to the Supreme Court's surprise ruling last week to free jailed politicians.