Foreign Affairs Minister Simon Coveney has said Britain is trying to link the issue of fishing "to a political narrative around sovereignty".
He also said that fish swim between territories, and that stocks caught in British waters are not labeled as 'British fish'.
It comes just four weeks before Britain's transition period out of the European Union ends, on December 31st.
He told The Pat Kenny Show: "As everyone will know, Ireland really wants a deal to be done here - but it's got to be a deal that both sides can live with.
"From our perspective we've got to make sure that Irish interests are part of any final deal, and that includes fishing".
It comes after the British Foreign Secretary Dominic Raab claimed "there is a deal to be done" as the EU and the UK enter the last week of "substantive talks."
Minister Raab claimed there is a "point of principal" when it comes to fishing rights.
"As we leave the transition, we are an independent coastal state," he said. "We have got to be able to control our waters.
"We can talk about transitions and things like that and we recognise the impact it has on other countries in Europe but that principal comes with sovereignty, comes with leaving not just the EU but the transition period.
"Can the EU accept that point of principal which comes with us leaving the political club?"
Mr Raab also dismissed the EU's current offer on fishing rights – in which the bloc's fishermen would return 15-18% of fish stocks caught by in British waters.
'It is not about sovereignty'
On the fishing issue, which Mr Coveney admitted is "highly emotive, very political", he said: "An agreement on fishing has got be agreed in the context of an overall agreement.
"And what I mean by that is the UK side are looking for the EU to facilitate them on access into EU markets for services, for financial services, for banking, for data, for aviation, for road haulage, they want to be able to access the EU's energy markets.
"And in return the EU is saying 'We'll facilitate a lot of that, but but we also want to have some access into your fishing grounds to ensure that we look after the interests of our fishing fleets'.
"So this is give and take - what the British side is trying to do is isolate fishing from everything else, to get deals on everything else, and then to accuse the EU side of being unreasonable on fish, linking it to sovereignty.
"It is not about sovereignty".
Mr Coveney said it is also not as simple as 'British fish in British waters'.
"For many months now the issue of fish has been part of an overall negotiation from an EU perspective, and the UK has constantly tried to separate fish to link it to a political narrative around sovereignty.
"Nobody is questioning British sovereignty post-Brexit, no one is questioning that the UK will control their own waters.
"What we looking for is an agreement that involves give or take".
Minister Coveney said such an example is that the EU is giving the UK access to its energy markets, which "doesn't undermine sovereignty".
"The truth also is that fish swim between sovereign territories: all the fish that are caught in British waters aren't 'British' fish, labeled British."
He gave an example that most of the mackerel caught off the Scottish west coast are actually born off the coasts of Cork and Clare.
"What we're saying is this is a shared stock and a shared resource that we need to manage in a way that sustainable for the stock and for the fishing industry".
He also suggested that "drawling lines" to divide EU and UK stocks in the North Atlantic is complex.
And Mr Coveney said other issues remain outstanding - including a level playing field.
"There's no way the EU can sign up to a trade deal that allows a future British government to - for example - use state aid in a way that creates competitive advantage for their own companies while selling into the EU single market."
He added: "If the UK wants a deal here, there's a deal to be done - if the UK wants to use fish as an excuse not to have a deal then that could happen to".