"But in this situation there is nothing else to do except to have an election and I will do my utmost so that elections will take place as soon as possible", Benediktsson said, as quoted by the Iceland Monitor media outlet.
Together the three parties held the slimmest of majorities 32 of the 63 seats in parliament following the October 29 election, which was called after the former prime minister resigned amid protests over his offshore holdings that were revealed in the Panama Papers leak.
Benediktsson said he would seek to continue as party leader, and that he believes the Independents can "gain strength" in an election.
The prime minister's father, Benedikt Sveinsson, wrote a letter to the Justice Ministry calling for the criminal record of a convicted sex offender to be erased.
The convicted friend is Hjalti Sigurjón Hauksson, who was found to be continually raping his stepdaughter on a daily basis since the age of five.
Prime Minister of Iceland Bjarni Benediktsson.
Benediktsson is a former finance minister who was also named in the Panama Papers as having offshore accounts.
The outgoing government would be the shortest-living in Iceland's history.
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Icelandic journalist Hjortur Gudmundsson said that the coalition is already fragile and another election would be a likely option.
It said in a Facebook post that there was "a serious breach of trust" behind its departure.
The Bright Future party has four seats in Iceland's parliament, the Althingi.
Although the justice minister Sigridur Andersen, of the Independence Party, told the prime minister of the letter in July, the government did not reveal its existence until a parliamentary committee forced it to a few days ago.
Mr Sveinsson has confirmed he signed a letter supporting his friend's application to have his "honour restored" by Iceland's judicial system.
A letter of recommendation is among the requirements to apply for the process.
Sveinsson said he had not discussed the letter with anyone.
"What was supposed to be a small gesture of good will towards a convicted criminal has instead turned into a continuation of the tragedy for the victim".