Claims over the vast estuary between Co Londonderry and Co Donegal have been made since the island was partitioned almost a century ago.
After the Good Friday Agreement, a cross-border body called the Loughs Agency was handed responsibility for the waters, a key strategic naval base during the Second World War.
But in the wake of the UK’s vote to leave the European Union, Northern Ireland Secretary of State James Brokenshire has reasserted London’s claim over the entire lough.
However, addressing the contentious issue after a meeting of the North South Ministerial Committee in Armagh, Charlie Flanagan said he did not accept the British claim.
He said: “This is an issue upon which there has been some disagreement for many years.
“I don’t accept the claims that the whole of Lough Foyle is under the jurisdiction of the UK government. However, rather than dwell on the negatives, I think it is important that we look forward and see how best this issue might be resolved.”
The minister said officials from his department had been in contact with civil servants from the secretary of state’s office in a bid to thrash out a resolution.
“I believe it is important that we work towards solutions and both myself and my department are committed to reaching a successful conclusion on this outstanding issue which has been the subject of disagreement for many decades.
“I do believe that we should work together on reaching agreement,” he said.
Meanwhile, Northern Ireland’s First Minister Arlene Foster said a barrier on the seas would contradict the efforts to avoid a hard border on land.
Mrs Foster said: “Obviously if there’s no hard border going to be on land we don’t really want to see a hard border on Lough Foyle either.
“There has been a dispute over Lough Foyle and it is important that we find a solution that everyone can agree on.”