Trade talks between the UK and the European Union will hit a crisis point unless there is progress the coming weeks, Minister for Foreign Affairs Simon Coveney has warned.

But he said the EU would not back down on its insistence that progress is made on fisheries and level playing field provisions in parallel to trade talks.

Mr Coveney was speaking after consulting with chief EU negotiator Michel Barnier ahead of EU-UK talks next Monday - one of two rounds remaining before the EU makes an assessment of progress in early July.

The EU's Brexit talks with British Prime Minister Boris Johnson's government were renewed late last month, but quickly hit snags, according to diplomats and officials in Brussels.

"The truth is that progress has not been good," Mr Coveney told RTÉ's Today with Sean O'Rourke.

"The necessary progress really isn't there.

"Unless there is significant progress in those negotiating rounds then I think we are going to reach yet another crisis point in the Brexit negotiations, which from the Irish point of view is very, very serious."

The end of June also marks the deadline for the two sides to extend negotiations beyond the end of the year, something the UK has ruled out.

A hard Brexit without a new trade deal in place is "a distinct possibility", Taoiseach Leo Varadkar predicted last week.

If the UK sticks to its refusal to extend, talks would need to be concluded by early November to allow time for ratification, Mr Coveney said.

When talks resume next week, the EU will continue to insist on progress on its priorities of fisheries and level-playing-field provisions, including in areas such as tax and state aid, in parallel to trade talks, the minister added.

"The UK seems to want to simply pick the areas where they want to deal early and solely focus on those," he said.

"The EU has made it very clear that that is not an approach that they can work with."

The UK, which is pushing for a basic free trade agreement, says the EU is making demands not sought from other trading partners. It says it will not accept measures that would tie it to European standards.

Implementation of the Northern Ireland protocol, which guarantees an open border on the island of Ireland, is "also important to build trust," Mr Coveney said on Twitter.