The Taoiseach has said both sides “need to dial down the rhetoric” on the Northern Ireland Protocol.
Micheál Martin said there are bound to be teething issues since the UK left the EU and calm is needed.
Mr Martin's comments come ahead of a meeting in London later on Thursday between the European Commission’s Vice President, Maros Sefcovic, and UK cabinet office minister Michael Gove to discuss the protocol.
Speaking on RTÉ’s Morning Ireland, Mr Martin said: “We need to dial down the rhetoric on both sides.”
He added that people need to bear in mind that it is only about six weeks since the Brexit deal was agreed.
“There are bound to be teething issues and teething problems and certain people were not as prepared as they could have been in relation to the implications of Brexit,” he said.
“We’ve witnessed that ourselves in the Republic, in respect of many companies not being as prepared as we might have thought they would have been.”
Mr Martin said the AstraZeneca dispute has reached “too high a pitch of a row” and that some member states need to “cool it” as well.
“I wasn’t too happy with the nature of the engagement over the last number of weeks,” Mr Martin said.
“I’m engaged with the president of the Commission on the protocol to see if we can fine-tune it, and work on it.
“I would say in the context of the island of Ireland and Northern Ireland and we all need to cool it down because I think that the debate around protocol got to too high a level, and tensions were rising unnecessarily.”
Asked about the deteriorating relationship between the Irish Government and unionists, Mr Martin said unionists need to “reflect and pull back” on the matter.
“Stand back from the nitty gritty and the teething issues that are undoubtedly there and they are there,” he said.
“I’m hearing what unionism is saying, they are under pressure, but they need to, I believe, take a different tack and look at this in a more constructive way for the future of the people on the island.”