Iceland's prime minister on Friday called for a second snap election in less than a year after a party quit the coalition government because he hid his father's involvement in seeking a clean record for a convicted paedophile.

Iceland Prime Minister Bjarni Benediktsson said he preferred the election to be held in November, just over a year after the last snap vote which was triggered by the Panama Papers scandal.

“It came as a considerable disappointment that we seem to be in the same place as after the general elections in 2016,” Benediktsson told a news conference in Reykjavik.

The government collapsed on Friday after Bright Future left the three-party, centre-right coalition, stripping it of its one-seat parliamentary majority.

“This situation was uncalled for but we will have an election... to let the voters decide,” Benediktsson said.

“It is impossible to put together a strong majority government which is what Iceland needs now,” Benediktsson later told AFP.

Bright Future accused Benediktsson of failing to inform the government that his father had signed a letter supporting a convicted paedophile's bid to have his criminal record erased after serving five and a half years in prison.

“I was shocked to hear that. I could never sign such a letter and I would never defend such a deed,” the 47-year-old Benediktsson said.

His father, an entrepreneur named Benedikt Sveinsson, had given support to a man who was convicted in 2004 of having raped his stepdaughter almost every day for 12 years.

'Breach of trust'

Iceland's previous government had collapsed over the Panama Papers scandal that embroiled several ministers and forced former prime minister Sigmundur David Gunnlaugsson to resign.

Benediktsson, whose name appeared in the Panama Papers scandal that revealed offshore tax havens, had delayed the release of a report on tax evasion during the legislative campaign.

The ruling coalition of the conservative Independence Party, led by Benediktsson, the centre-right Reform Party and the centrist Bright Future, was formed only nine months ago after the October vote.

Bright Future said earlier Friday that its executive committee “decided to terminate the cooperation with the government” because of a “serious breach of trust”.

Benediktsson said the announcement came as a “total surprise” and “a great disappointment”.

“I consider it a sign of weakness by those who desert (the government)”.

'Knocked on doors for favours'

The situation has intensified a fierce public debate over the procedure for rehabilitating convicts, which does not change or reverse a verdict, that had flared in recent weeks over another convicted paedophile who was granted an expunged record.

The convicted child molester supported by Benediktsson's father had applied after serving his sentence for “restored honour”, which would enable him to expunge his criminal record.

It is permitted under Icelandic law and is subject to the support of persons of good character.

But now more and more Icelanders see it as a blow for victims.

The Icelandic Women's Rights Association said the government collapsed because women were willing to make their voices heard.

“People spoke out about violence which women and children were subjected to. People spoke out when convicted abusers knocked on their friends' doors to ask for favours,” the association said in a statement.

A spokeswoman of the Pirate Party on Friday called for an urgent vote for constitutional reforms, without specifying the changes it sought.

“The Pirate Party calls on all other parliamentary parties to comply with this call and invites the president of Iceland ... to approve a new constitution before the parliamentary assembly is suspended,” Birgitta Jonsdottir wrote on Facebook.