"I sincerely accept my defeat in the election. We lost the election because 5,000 citizens said they want people other than us to lead the government," said Nasheed, candidate from the Maldivian Democratic Party (MDP).
Nasheed said MDP should now focus on becoming "an opposition party loyal to the state".
"I am defeated, that I have to accept," Nasheed said. He said MDP will not incite violence.
He said his party will also focus on winning the parliamentary election.
Abdulla Yameen from the Progressive Party of Maldives won the second round of the Maldivian presidential election, initial results showed.
Former president Nasheed, who got 46 percent of the votes in the first round Nov 9, was facing Yameen in the run-off.
Yameen received 29 percent in the first round and is endorsed by third-placed Jumhoory party candidate Gasim Ibrahim, who received 23 percent of the votes.