Iceland's government has collapsed after a coalition partner resigned after learning the prime minister's father was trying to clear the name of a convicted paedophile.

The centrist Bright Future party said in a Facebook post that 'a serious breach of trust' prompted its departure.

Prime minister Bjarni Benediktsson took office in January with his Independence Party, the Reform Party and the centrist Bright Future party.

Mr Benediktsson's father, Benedikt Sveinsson, helped a convicted child molester apply for a clause in Iceland's judicial system which allows a person who has served their sentence for a serious crime to 'restore their honour' and seek employment again.

Prime minister Bjarni Benediktsson's father, Benedikt Sveinsson, helped a convicted child molester apply for a clause in Iceland's judicial system which allows a person who has served their sentence for a serious crime to 'restore their honour' and seek employment again. Pictured: PM Bjarni Benediktsson

In 2004, Hjalti Sigurjon Hauksson was convicted of raping his stepdaughter almost every day for 12 years, and sentenced to five years in prison.

When it emerged that some government members, including its head, had kept information from the public about a letter seeking to expunge Hauksson's record, the Bright Future party said it was quitting.

The Bright Future party has four seats in Iceland's parliament, the Althingi. Its resignation from the government will likely prompt an election.

Together the three parties hold the slimmest of majorities - 32 of the 63 seats in parliament - following elections last October after the former prime minister resigned amid protests over his offshore holdings, revealed in the Panama Papers leak.

It is unclear whether Mr Benediktsson, a former finance minister who was also named in the Panama Papers as having held a stake in a Seychelles-based investment company, will seek to form a new coalition or will call new elections.

Iceland, with a population of 320,000, suffered years of economic upheaval after the country's debt-swollen banks collapsed during the 2008 global financial crisis.