The chain owns the European trademark use for the name, which Icelandic officials claim the firm defends "aggressively".
Businesses in the Nordic country say it means they find it difficult to use the term to describe goods and services from their own homeland.
The store said it is sending a team to Iceland this week for talks.
"We registered Iceland as our company name in 1970 and we have coexisted with the country called Iceland very happily ever since," insisted company founder and chief executive Malcolm Walker.
"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 that there is ample scope for an agreement that will allow both parties to continue to live and work amicably alongside each other."
The Icelandic government mounted a legal challenge against the food store at the European Union Intellectual Property Office last week.
It described the current situation as "untenable" and had "caused harm to Icelandic businesses, especially its small and growing companies".
The supermarket chain, which has its head office in Deeside, Flintshire, said the outbreak of "legal and verbal hostilities" last week was regrettable.
The company has has more than 800 stores across the UK and employs more than 23,000 staff.
Officials at the store stated they had "a long history of close and friendly involvement" with the country, including seven years being run by Icelandic investors until a Â£1.5bn management buyout in 2012.
The store said the relationship with its namesake country continued to be reflected through the ownership of three Iceland stores there, export sales of Iceland products to other retailers throughout the country, and sponsorship of the Icelandic national team in this year's European football championships.
Mr Walker added: "A high level delegation from Iceland - the company - is preparing to fly to Reykjavik this week to begin negotiations, and we very much hope for a positive response and an early resolution of this issue."
Supermarket Iceland says it wants talks with the Icelandic government in the legal battle over the store's name.