Businesswoman Halla Tomasdottir was set on Sunday to become Iceland's new president, election results showed, beating former prime minister Katrin Jakobsdottir, who critics said was too political for the post.

Jakobsdottir conceded defeat early on Sunday and congratulated Tomasdottir, the CEO of The B Team, a global non-profit co-founded by UK business tycoon Richard Branson to promote business practices focused on humanity and the climate.

Iceland's president holds a largely ceremonial position in the parliamentary republic, acting as a guarantor of the constitution and national unity.

He or she does however have the power to veto legislation or submit it to a referendum.

Tomasdottir, 55, was officially credited with 34.6 percent of votes, after 71.6 percent of ballot papers had been counted on Sunday.

The 48-year-old Jakobsdottir, who stepped down as prime minister of a left-right government in April to run in Saturday's election, garnered 25 percent.

The results showed Tomasdottir with much stronger support than opinion polls had suggested in the run-up to the election, where the two candidates had been seen running neck-and-neck.

The final results were likely to change somewhat but Jakobsdottir conceded defeat in the early hours of Sunday before the last votes were in.

"It seems to me that Halla Tomasdottir is quickly heading towards becoming the next president of Iceland.

"I congratulate her on that and know that she will be a good president," Jakobsdottir told national broadcaster RUV at an election night rally.

- Second woman president -

Tomasdottir meanwhile told daily Morgunbladid during her election rally she was "just trying to breathe".

"I feel incredibly good. I know it's not over until it's over. So I'm also just trying to stay calm and breathe," she said.

Tomasdottir is also the founder of Audur Capital, an investment firm created in 2007 aimed at promoting feminine values in the financial sector.

No one central issue dominated the campaign, where candidates traditionally run as independents without party affiliations.

In the country of 380,000 people, any citizen gathering 1,500 signatures can run for office.

While Jakobsdottir was at times seen as the favourite, political observers had suggested that her background as prime minister could weigh against her.

Among the other main candidates in the field of 13 were a political science professor, a comedian, and an Arctic and energy scholar.

Tomasdottir is set to be the second woman to serve as Iceland's president.

In 1980, Vigdis Finnbogadottir became the world's first woman democratically elected as head of state.

The businesswoman is set to succeed the hugely popular Gudni Johannesson, who has held the job since 2016.

He announced earlier this year that he would not seek re-election.

Jakobsdottir, party leader for the Left Green Movement from 2013 until her presidential bid, has been hailed for her handling of the resurgence in volcanic eruptions on the Reykjanes peninsula since December.

The five eruptions, including one last week, have sparked a series of evacuations as well as the state's acquisition of homes from residents evacuated from the threatened fishing town of Grindavik.