And now Iceland Foods is seeking to smooth over any grievances, saying it seeks "peaceful coexistence" with the country.
In a statement, the company said: "Following the regrettable outbreak of legal and verbal hostilities last week, the UK retailer Iceland Foods is urgently seeking a meeting with the foreign ministry of Iceland to lay out constructive proposals for resumption of the peaceful coexistence between the company and country that had prevailed for the previous 46 years."
It all got chillier than London's current temperature last week when the country confirmed it was actually taking legal action against the supermarket, so its own producers can use the word Iceland when advertising their own food products. A legal challenge has been lodged at the European Union Intellectual Property Office against Iceland Foods' Europe-wide trademark for the word Iceland.
The country thinks that should be invalidated as it's too broad and ambiguous in definition, "often rendering the country's firms unable to describe their products as Icelandic".
Now Iceland Foods wants to make clear it didn't just snap up its name from the Nordic nation "but has a long history of close and friendly involvement with Iceland the country". Not so warm now though.
For seven years from 2005, the supermarket was under the control of Icelandic investors and then banks, which came to an end with a £1.5bn management buyout in 2012.
Iceland founder and chief executive Malcolm Walker, said:
They have made no contact with us to raise any concerns about trademark issues since 2012.
We have no desire whatsoever to stand in the way of Iceland (the country) making use of their own name to promote their own products, so long as it does not conflict or cause confusion with our own business.
I am sure there is ample scope for an agreement that will allow both parties to continue to live and work amicably alongside each other.
The company is sending out a delegation to Reykjavik this week to begin negotiations.
But it might be in for a cool reception.
The government of Iceland said in a statement it would "welcome an agreement" with Iceland Foods, with the supermarket withdrawing its exclusive trademark of the word.
"Iceland Foods has since 2012 taken legal action against multiple companies from Iceland that use our country's name to describe themselves," it said. "The government of Iceland seeks to ensure that businesses and products from Iceland can be proud of our home and can reference their country of origin."