The health risks and benefits have been a topic of debate for several years in some European countries, although none have banned the practice outright.
Iceland, which has a population of around 334,000, has a small Muslim population of a few hundred people, and an even smaller Jewish population of around 100 people.
While Iceland has no designated Rabbi, Jewish news source ynetnews.com reports that Chief Rabbi of Denmark Yair Melchior and the Rabbi of Oslo, Yoav Melchior are campaigning against the bill on behalf of the Jewish population in Iceland.
"Iceland does not have a significant Jewish or Muslim population; therefore there are hardly any opponents to the bill. Only considerable international pressure can help," the Rabbis told ynetnews.
"There is no country in the world now that bans circumcision. This sets a dangerous precedent that may affect other countries; the Danish parliament is now considering such a bill as well," they added. The Danish Medical Association has advised against male circumcision in boys for several years, though no ban has been enacted in the country.
The European Conference of Rabbis also voiced their opposition to the bill in a statement, as reported in ynetnews.
"Circumcision is a critical part of Jewish life and no authority in the world can forbid Jews from carrying out this commandment," they said.
Rabbi Pinchas Goldschmidt, president of the group, added that "although the Icelandic Jewish community is small, we cannot ignore the dangerous precedent that this law can set and the consequences that such legislation can cause in other countries."
"We call on lawmakers to immediately rescind this miserable piece of legislation and continue supporting Jewish life without limits."
It is unclear when the bill would be up for a vote.