Iceland's minister for children has resigned after admitting she had a child with a teenager more than 30 years ago.

Ásthildur Lóa Thórsdóttir said in a media interview she had first started a relationship when the boy was 15 years old, and she was a 22-year-old counsellor at a religious group which he attended.

She then gave birth to his child when he was 16 years old and she was 23.

"It's been 36 years, a lot of things change in that time and I would definitely have dealt with these issues differently today," the 58-year-old told Icelandic media.

Iceland's prime minister, Kristrún Frostadóttir, told the press this was "a serious matter", although she said she knew little more than "the average person".

"This is a very personal matter [and] out of respect for the person concerned, I will not comment on the substance," she said.

According to Visir newspaper, Frostadóttir said she had only received confirmation of the story on Thursday night.

She immediately summoned the children's minister to her office, where she resigned.

Icelandic news agency RUV broke the story on Thursday night.

Thórsdóttir revealed in an interview with them that she had met the father, who RUV name as Eirík Ásmundsson, while she was working at the religious group Trú og líf (Religion and Life), which he had reportedly joined because of a difficult home life.

He was 15 years old and she was 22 at the time of their meeting. Thórsdóttir gave birth to their son when they were both a year older.

RUV report that the relationship was secret, but that Ásmundsson was present at his child's birth and spent the first year with him.

However, the news agency writes this changed when Thórsdóttir met her current husband.

They report they have seen documents Ásmundsson submitted to Iceland's justice ministry requesting access to his son, but that Thórsdóttir denied it, while also requesting - and receiving - child support payments from him over the following 18 years.

A relative of Ásmundsson tried twice to contact the Icelandic prime minister about the relationship last week.

Frostadóttir said last night that when the woman revealed it involved a government minister she asked for more information, which led to the revelation and the resignation.

In her TV interview with RUV last night, Thórsdóttir said she was upset that the woman had contacted the prime minister.

"I understand... what it looks like," she said, adding that it is "very difficult to get the right story across in the news today".

While the age of consent in Iceland is 15, it is illegal to have sex with a person under the age of 18 if you are their teacher or mentor, if they are financially dependent on you, or work for you. The maximum sentence for this crime is three years in jail.

Despite resigning from her ministerial job, Thórsdottir said she had no plans to leave parliament.