"President Waheed.. has called for elections in July 2013, the earliest date permitted under the Constitution," his office said in a statement on Wednesday.
Under the current constitutions, elections were due in October 2013. However, former president Mohamed Nasheed, who claims he was forced out of office in February, has been calling for elections this year. His call has been backed by the Commonwealth and India, who have been trying to mediate in the political crisis since Nasheed's hurried resignation.
Waheed, who was the vice-president under Nasheed, has appointed a committee to probe the events that led to Nasheed's controversial exit.
The new president has since formed a coalition government, and won his first popularity test during Saturday’s elections.
A former UN diplomat, Waheed did not directly field candidates, but endorsed members of his coalition partners for the Thimarafushi and Kaashidhoo constituencies and both won comfortably, the Elections Commission results showed.
Government-backed Progressive Party of Maldives (PPM) candidate Ahmed Shareef won Thimarafushi constituency with 1,755 votes while former president Mohamed Nasheed's Maldivian Democratic Party (MDP) got only 1,327.
In Kaashidhoo, the Jumhoory Party candidate who was supported by Waheed won with 1,107 votes while the MDP candidate managed only 784.
The election was for two seats in the 77-member People's Majlis.
More than 85 percent of the 6,000 electorate turned out to vote, official results showed. The voting was peaceful, elections commission spokesman Mohamed Tholal said.
The by-elections were called after the country's highest court recently disqualified the MPs elected in elections in 2009.
Nasheed, who has gain international fame as a climate change campaigner, was elected the first democratically elected leader in the Maldives following the nation's inaugural multi-party elections in October 2008.
However, the 2009 legislative elections led to a hung parliament.
Sarturday's vote is unlikely to change the impasse in parliament.
Nasheed's Maldivian Democratic Party remains the largest single group with 32 seats, while the DRP, a party launched by former president Maumoon Abdul Gayoom controls 24.
Nasheed and his Maldivian Democratic Party say Waheed’s government is illegitimate and have taken to the streets demanding his resignation and an early poll.
In February, the Commonwealth group of mostly former British colonies, suspended the Maldives from its democracy watchdog group and has backed early elections to end any question over the legality of the transfer of power.
There was no immediate comment from the Commonwealth or Nasheed's party on Waheed's offer for early elections next July.