"Maldives authorities have detained critics, muzzled the media, and misused the election commission to obstruct opposition candidates to ensure President Yameen a victory on election day", said the group's Asia associate director Patricia Gossman.
The Opposition Leader, Mr Solih, told supporters he was confident of victory.
"The message is loud and clear". The people of Maldives want change, peace and justice.
"I call on Yameen to respect the will of the people and bring about a peaceful, smooth transfer of power", Mr Solih said on national television shortly after official results showed he had an unassailable 58% of the popular vote. The provisional results for the remaining 9 per cent of the vote have yet to be announced.
Yameen was expected to cement his grip on power amid criticism over the fairness of the vote on the islands best known as a luxury holiday destination.
"It is crucial to note that as a lawmaker Ibu has enjoyed cross-party appeal more than any other", said Azim Zahir, a Maldivian researcher based in western Australia.
The Election Commission said it will release official results by September 30, as stipulated in the constitution.
Voting in the Maldives presidential election ended later than expected on Sunday, after polling stations were ordered to stay open for an extra three hours to deal with a large voter turnout.
"If we win or lose, PPM has the courage to accept the decision of Maldivian people", the ruling party's parliamentary leader MP Ahmed Nihan wrote on Twitter.The Muslim-majority Indian Ocean nation has become a theatre of rivalry between its traditional partner, India, and China, which has backed Yameen's infrastructure drive, and prompted concern in the West about Beijing's increasing influence.
Mr Yameen has imprisoned many of his main rivals, controls the country's courts, and is accused of leasing islands off to developers in secret, with much of the proceeds going to government cronies instead of government coffers.
"I don't agree with the policies of this government and also some corrupt activities", said 19-year-old Scifulla Waheed, who is looking to vote for the first time on Sunday.
Hundreds waited in line as a light rain fell in Maldives' capital, Male.
Gayoom has been criticized for cracking down on freedoms.
Yameen told supporters on the eve of the election he had overcome "huge obstacles" since controversially winning power in a contested run-off in 2013, but had handled the challenges "with resilience".
Most poll monitors, including those from the European Union and United Nations, declined the government's invitation to observe the election, fearing their presence might be used to endorse Yameen's re-election even after possible vote rigging.
Rohana Hettiarachchi, a member of the Asian Network for Free Elections (ANFREL), which was named as an election monitor, said his organisation could not take part.
Some 262,000 people in the archipelago - famed for its white beaches and blue lagoons - were eligible to vote in an election from which independent worldwide monitors have been barred.
"It's a worry for us here in Australia that we've got another country that is slipping down quite rapidly the slope towards quite a brutal dictatorship".
Observers from Transparency Maldives said in a statement late Sunday morning that opening procedures "went well", with almost all of the polling stations opening within 30 minutes of the scheduled opening time.