Riding a wave of popularity based on defying Britain and the Netherlands over collapsed Iceland banks, Olafur Grimmson looks set to become president for a record fifth time.
Grimmson vetoed a bill proposing to pay almost four million euros to Dutch and British savers who lost out when Landsbanki collapsed in 2008.
One of his rivals for the presidency was politically-inexperienced television journalist Thora Arnorsdottir.
The 37-year-old, who interrupted her campaign in May to give birth to her third child, conceded defeat on Saturday. She says she has no plans to run again in four years.
Once the official results are announced, Grimmson will continue in the top job he has held since 1996.
The presidency is meant to be a largely ceremonial role, but Grimmson’s decisions have brought a political edge to it over the years.