He also met with businesses and regional representatives
Tánaiste Simon Coveney has said the Government wants to see significant progress on "an operable, legal text" on any backstop option for the Irish border by June.
He was speaking from Co Derry, where he addressed the Chamber of Commerce President's Lunch.
He also met with businesses and regional representatives in the North West region.
The Foreign Affairs Minister also met with civil society groups in the city and visited the Museum of Free Derry.
He said: "I was very pleased to address the Londonderry Chamber of Commerce today to outline the Government's priorities and engagement to address the risks of Brexit for the island of Ireland, and also on working with the British government and the political parties in Northern Ireland to find a way beyond the current impasse with the devolved institutions".
"We also spoke about the impact of Brexit on organisations in the North West region, and what businesses have been doing to ensure they are Brexit-ready, as well as progress on a number of regional issues.
"It was a really useful opportunity to update members of the chamber on progress in the EU-UK negotiations and to outline the Government's key priorities in that process."
"I encouraged representatives at the chamber event to stay engaged on Brexit issues, and I look forward to their continued participation in stakeholder engagement opportunities over the coming months."
But Minister Coveney said progress has to be made on the border - or any backstop agreement - by the summer.
"A border region with two jurisdictions that are co-operating really well with each other - between Letterkenny and Derry - in a way that is mutually beneficial for everybody.
"Sharing health services, GP services, education facilities - and that's what we want to maintain in the future".
"We're not asking for everything to be finalised by June, but we do expect to see significant progress on an operable, legal text that reflects the commitments that were made in December - which deals comprehensively with putting a backstop in place to ensure that there will be no border infrastructure on the island of Ireland".
The chief Brexit negotiator for the European Union, Michael Barnier, has previously said a backstop solution "must apply" unless and until another solution is found.
The 'backstop' refers to an earlier deal reached between the UK and EU in December, saying a "common regulatory area" will be established in Northern Ireland following Brexit if no other solutions to the border issue can be found.
It comes as the UK's Brexit Secretary David Davis said there is more chance of a withdrawal deal with the European Union than there is of not getting one.
He appeared in front of MPs to answer questions earlier on Wednesday.
He was asked if ministers would abandon leaving the customs union if they did not get the backing of most MPs.
"The government always respects parliament - but I expect the government's policy to be upheld for good reason".