The songwriter however failed to reach 40 per cent of the votes so will now have to compete in the runoff on 1st April against ex-government minister Carlos Alvarado Quesada, who was also once a singer in a rock band.
The 43-year-old from the evangelical National Restoration Party, became widely popular candidate after denouncing a court ruling calling on the Central American country to give civil marriage rights to same-sex couples.
He has threatened to pull Costa Rica out of the court, which is based in the capital, San Jose.
"People said, 'This is the person that I want to defend us in the face of international impositions'," he told a Costa Rican radio station after he took the lead in opinion polls.
While the country is deeply Catholic, evangelical Christianity has emerged as a religious and political force in recent years.
In all, 13 candidates ran to replace President Luis Guillermo Solis of the centre-left Citizen's Action Party (PAC).
Final first-round results will be published later on Monday.
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