The Maldivian Democratic Party (MDP) had criticised the Supreme Court's sacking of the elections chief and his deputy just before Saturday's election, but nevertheless decided to face the polls.
"How can we call this a free vote when the Supreme Court sacks the chief elections commissioner and his deputy two weeks before the election?" MDP spokesman Hamid Abdul Ghafoor told AFP. "But, we concede defeat."
The commission's top two have yet to be replaced and President Abdulla Yameen himself raised doubts on Thursday if the election could be held by a depleted panel of three.
However, early projections by the Haveeru newspaper placed Yameen's Progressive Party of Maldives (PPM) as the largest single party with 34 seats in the 85-member assembly.
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Its allies were predicted to win a further 21 seats, making a PPM-led coalition a formality.
The MDP secured 24, according to Haveeru figures and party spokesman Ghafoor said they accepted the paper's projections as being a fair reflection of Saturday's first-past-the-post election.
Nasheed's nemesis, former Maldivian strongman president Maumoon Abdul, congratulated his half brother Yameen on his party's "impressive victory".
The independent watchdog Transparency Maldives said the election was conducted well, but alleged widespread "vote buying" that it said could undermine democracy in the long run.
It did not say which party or candidates were buying votes.
Saturday's poll went ahead as scheduled despite fears about the ability of the elections commission to stage the ballot successfully after the two sackings by the Supreme Court.
Just over two-thirds of the 240,000-strong electorate turned out to vote, officials said, citing preliminary estimates.