"I found the statement from the Nordic ombudsman of children from 2013 where they encourage all the Nordic states to ban circumcision on boys as it goes against the UN convention on the rights of the child,” she told SBS News.
“So I put the bill forward to protect children first and foremost because I think the rights of the child should be taken further than the rights of an adult to believe whatever an adult wants to believe in."
The legislation would jail those found guilty of performing the procedure for non-medical reasons for up to six years.
Ms Gunnarsdóttir introduced the bill along with MPs from four other parties.
Male circumcision is considered important in many religions - particularly in Judaism and Islam - with around a third of men believed to be circumcised globally.
Ms Gunnarsdóttir said she believes this reason in particular has stopped many countries from going down a similar route to Iceland.
“Of course I speak for religious freedom but I think you can’t take the rights of another person as protecting your own rights to believe in something,” she said.
“Circumcision can be a risky procedure, it’s non-reversible, it’s totally unnecessary, so I think on those grounds we should think carefully about this.”
I use the slogan "his body, his choice", I think that sums it up. It's not about the intention of the doing, it's about the children.
Imam Ahmad Seddeeq from the Islamic Cultural Center of Iceland said the bill is tantamount to religious oppression.
He said it hinders participating in Muslim and Jewish culture, and is “widely practised in the whole world regardless of even being religious or not, because it's healthy as doctors say about this."
'It's about the children'
A recent study released by the University of Sydney's Dr Brian Morris stated the benefits of male infant circumcision exceeded the potential risks by 200 to one.
Furthermore, it claimed that uncircumcised males faced an 80 per cent risk of requiring medical attention due to their condition.
Cosmetic circumcision is banned at Australian public hospitals, but can be done privately.
Professor Paul Colditz from the Royal Australasian College of Physicians said the number of males being circumcised - in Australia and globally - is falling, which could be at least partly attributed to the better availability of information.
But he is sceptical that moves similar to Iceland's ban could happen here.
"We assign to parents the right to make decisions about their child's health, and where there is evidence neither strongly in support or not in support of a particular medical procedure, then that overriding responsibility is going to take precedence, he said.
“That's fortunate because it lines with up the very multicultural society that we live in where there are different views on circumcision."
Icelandic parliamentarian Silja Dögg Gunnarsdóttir doesn't want to predict if the proposed bill will pass or not.
But she said her belief that she’s doing the right thing has been reaffirmed by the overwhelming support she’s received from around the world.
"I have had so, so many letters from all over the world. I have had letters from mothers, from men who were circumcised and they tell me they would never have done it if they had had the chance to choose themselves. I have had letters from Muslims, Jews, Christians, non-believers, people who have been circumcised and they all say the same and they support the bill and I have had a lot of positive responses and support. I think only one or two letters from Australia and they were also supporting the bill.”
“I use the slogan "his body, his choice", I think that sums it up. It's not about the intention of the doing, it's about the children."