The second round of voting will take place on August 7 on the island nation officially known as Sao Tome and Principe.
Sao Tome sits in the oil-rich Gulf of Guinea region but the country’s new leader will need to revive oil hopes after results from initial exploration wells disappointed investors.
Provisional results showed da Costa leading with 35 percent of the vote ahead of de Carvalho on 21 percent, election commission chief Victor Correia said on Monday.
After scoring 14 and 13 percent respectively, former prime minister Maria da Neves and opposition member of parliament Delfim Neves will potentially play king-making roles in the election run-off.
Da Costa ran the country from independence in 1975 until 1991 and has maintained close relations with nearby Angola, which has made significant investments in the country.
De Carvalho is a member of the ADI party which won the most votes in last year’s parliamentary elections and has the backing of current Prime Minister Patrice Trovoada.
About 60,000 of the country’s more than 92,000 registered voters cast their ballots in Sunday’s poll. The election commission said there were no reported problems.
Current President Fradique de Menezes is stepping down as he is coming to the end of his second, five-year term.
The former Portuguese colony is trying to attract more tourists to its largely unspoilt, palm-fringed beaches. It also has a small cocoa sector.