Scottish and Irish governments have agreed to "intensify" discussions to resolve a row over fishing off Rockall.
Irish fishing boat crews have been accused of making incursions into Scottish territorial waters 12 nautical miles around the North Atlantic islet.
Scotland's External Affairs Secretary Fiona Hyslop said Scottish fishing rights would be protected.
Taoiseach (Irish prime minister) Leo Varadkar said the fishing grounds around Rockall were part of EU waters.
"I think that the fisheries and territories around it should be shared," he told the Irish parliament. "The Irish vessels in those waters have EU quota and these waters are part of EU waters.
"And under the Common Fisheries Policy we believe they are in their rights to continue to fish in the area around Rockall."
Mr Varadkar added: "Rockall is a rock, essentially a sea stack in the middle of the ocean. It's uninhabitable, uninhabited and I don't think it is something that Ireland and Scotland should fight over.
"We don't have a claim on it. We don't accept any other sovereign claim on it.
"I think it is fair to say that both administrations would like to see this matter de-escalated."
A statement from the Irish government added: "Dialogue regarding Rockall is continuing between the Irish and Scottish governments.
"There have been close contacts at official level over recent days. It has now been agreed that a process of intensified engagement will take place, led by senior officials from both administrations."
The Scottish government previously said it was sure of its legal position.
Ms Hyslop said Ireland had been notified of enforcement action if Irish boats were found in Scotland's territorial waters.
She told MSPs at Holyrood that Scotland valued its relationship with Ireland.
She said senior officials involved in talks to resolve the dispute had agreed to "intensified engagement". Ms Hyslop said ministerial channels also remained open.
The minister told MSPs that incursions into the waters around Rockall had increased from 15 in 2015 to 33 in 2016 and 94 in 2017.
There was a slight decrease in 2018 due to changes in fishing quotas and the absence of some fish, she said.
Marine Scotland is monitoring activity around Rockall using aircraft and satellite images.
Earlier this week, John O'Kane, of Greencastle Fishermen's Co-Operative, said three Irish skippers would continue to fish in the area, as they had done for the past 30 years.
Speaking to RTÉ, Mr O'Kane said the Irish boats had been operating inside the 12-nautical mile zone.
Rockall, an eroded volcano, lies 260 miles (418km) west of the Western Isles.
Its fishery is a multi-million pound fishery, with several species of fish including haddock, monkfish and squid.
The islands' SNP MSP Alasdair Allan, who raised the matter at Holyrood, said waters around the islet were important to fishing crews in his constituency.