In a Facebook campaign launched by Icelandic author, Bryndis Bjorgvinsdottir, some 12,000 people - 4% of the Icelandic population - offered to welcome refugees into their homes.
That sum would be the equivalent of 2.6 million Brits.
It is estimated that more than 340,000 refugees have made their way to Europe so far this year - nearly three times the number who arrived in the first seven months of 2014.
In a post at the top of the Facebook page, addressed to Icelandic Minister of Welfare, Eygló Harðar, 33-year-old Bjorgvinsdottir wrote: "The idea is to show the government that there exists a will to receive even more refugees from Syria than the 50 that have already been discussed.
"We want to push the government – show them that we can do better, and do so immediately.
"In 1973 we received 4,000 refugees from the Westman Islands overnight after a volcanic eruption, when everyone helped – and we should not forget the number of foreign volunteers that came to the country to help then.
"Refugees are human resources, experience and skills. Refugees are our future spouses, best friends, our next soul mate, the drummer in our children’s band, our next colleague, Miss Iceland 2022, the carpenter who finally fixes our bathroom, the chef in the cafeteria, the fireman, the hacker and the television host.
"People who we'll never be able to say to: 'Your life is worth less than mine.'"
To date, 12,000 people have joined the campaign, with a range of offers being posted on the Facebook page.
Icelandic citizens have volunteered their services to cook for those in need, take children to school, donate clothing and kitchenware and helping Syrian refugees to "adapt to Icelandic society".
The response to the campaign has prompted Iceland's Prime Minister Sigmundur David Gunnlaugsson to appoint a new committee to address the possibility of allowing more refugees into the country, the Icelandic Review Online reports.
“It has been our goal in international politics to be of help in as many areas as possible and this is one of the areas where the need is most right now,” Sigmundur said.
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The reactions from European state leaders to refugees on the continent have varied widely.
Czech President Miloš Zeman was criticised following comments he made at a press conference on Sunday, in which he compared desperate refugees to "a tsunami that will kill him".
He had suggested that a huge wave of migrants would cripple and destroy the Eastern European country because "refugees will invite their relatives to join them".
On Tuesday, Labour leadership hopeful, Yvette Cooper, said that Britain should accept at least 10,000 refugees to tackle the worst humanitarian crisis in Europe since the Second World War.
Cooper called on towns and cities across the country to each take in ten migrant families as part of the UK's effort to help the thousands fleeing war-torn countries.
In the meantime, Germany is preparing itself to for 800,000 asylum applications this year - four times the number it received in 2014.