Party leaders took the dramatic decision to quit the center-right government after it emerged Mr. Benediktsson's father had written a letter recommending a convicted pedophile's name be cleared.
Leaders of Bright Future, a junior partner party in the government, have ended their coalition with the Independence Party and its Prime Minister Bjarni Benediktsson, according to the online newspaper Iceland Monitor.
The Reykjavik Grapevine reports that Hjalti Sigurjón Hauksson was convicted of having repeatedly raped his daughter over 12 years while she was a child & teenager.
A letter of recommendation is among the requirements to apply for the process.
The Ministry of Justice had previously refused to reveal who wrote the letter, Reuters reports, which has now led to allegations of an attempted cover up.
"The board of Bright Future has chose to terminate cooperation with the government of Bjarni Benediktsson", the party said in a statement on Facebook.
"I think if there's going to be another election and possibly the chance of a more left-wing government, then that probably decreases the chance of monetary policy being loosened any further in the future", said Brown.
Magnus Sveinn Helgasson, managing editor of Iceland Magazine, told Sputnik the affair could eventually result in a major shake-up of the political scene in Iceland.
"It would not necessarily be a surprise if the prime minister wants to call an election", said Baldur Thorhallsson, a political scientist at the University of Iceland. He may try to continue or he could decide to call an election, we don't know. "It is all extremely unusual". Together, the three-party coalition holds a slim majority with 32 seats.
Opposition groups such as the Left-Green Movement and the Pirates party have now called for an election in the wake of the government's collapse.
"I have never considered the restored honour as anything except a legal procedure making it possible for convicted criminals to regain some civil rights", he said in a statement released on Thursday.
"Since the economic crash of 2008 there has been a lot of suspicion towards politicians and a huge onus on honesty", he said.
That leaves the country, whose economy was wrecked by the collapse of its banking sector almost a decade ago, possibly facing its second snap election in less than a year after the previous government was felled by the Panama Papers scandal over offshore tax havens.
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