The open letter written to the country's welfare minister said it wanted to show "the government that there exists a will to receive more refugees from Syria".
Has the campaign been welcomed?
Bjorgvinsdottir's letter has been signed by around 13,000 people so far, with some pledging to welcome Syrian refugees into their home and others offering to donate clothes and money to the refugees.
That's a lot of people.
It is, considering the country's population is 323,000. Single mother Hekla Stefansdottir, who has a sixyear-old son, said: "We can take a child in need. I'm a teacher and would teach the child to speak, read and write Icelandic."
Has the Icelandic government changed its tune then?
Welfare minister Eyglo Haroardottir told RUV that the government would explore avenues to welcome more humanitarian refugees but would not name a maximum figure for its quota. At a cabinet meeting which took place yesterday, Prime Minister Sigmundur Davio Gunnlaugsson set up a special committee of ministers to discuss issues regarding migrants and how Iceland could respond.