President Higgins has said he believes the good relations that exist between Ireland and Britain will continue "no matter what happens" in relation to the ongoing Brexit negotiations.
He said it is crucial that any deal reached between the UK and the European Union secures the position of the Good Friday Agreement.
Speaking on the third day of his state visit to Cyprus, the President said: "We will still be neighbours no matter what happens. I think the good relations we have established over the years will prevail.
"I do think it is very important that the outcome be one that secures the position in relation to the peace agreement, that enables the economy to continue to function in both of the interests of north and south.
"As well as that east and west, that there would be minimum disruption to trade and that's to the benefit of both the United Kingdom and ourselves."
President Michael D Higgins has said he believes the good relations between Ireland and the UK will continue "no matter what happens" in relation to Brexit | Read more: https://t.co/P4ab4RjX6o pic.twitter.com/MB6uyA3JxM— RTÉ News (@rtenews) October 16, 2019
Earlier, President Higgins spoke in strong terms about the distress and hardship caused by the imposition of austerity measures on countries within the EU.
He said policies imposed during the financial crisis facilitated "the rise of euro-scepticism" and "exclusionary forms of nationalism".
The President made his comments during an address to the House of Representatives in Cyprus.
Referring to the impact of the global crisis on EU member states such as Cyprus and Ireland he said: "It is clear now that, as a direct result of the blunt impositions and handling of the crisis, social cohesion has been significantly damaged across our Union.
"This has a consequence in its contribution to an atmosphere that facilitated the rise of euro-scepticism, exclusionary forms of nationalism and austerity-sourced populism, nativism, reactions that are built on negative invocations of fear and ignorance, including a fear and ignorance that is invoked and manipulated too often to scapegoat the stranger, 'The Other'."
Mr Higgins' visit to Cyprus marks the first State visit to the island by an Irish President since President Mary McAleese in 2006.
During the address to the parliament, he took the opportunity to highlight the role played by Irish peacekeepers on the island.
President Higgins praised the work of over 10,000 Irish soldiers who have served in Cyprus since 1964, as well as the ongoing presence of 12 members of An Garda Síochána.
"As a nation which has known division and tension, Ireland is well equipped to understand the complexities of the circumstances here in Cyprus. I am immensely proud of the work carried out by the Irish women and men who have served here, and of the genuine bond they have helped to create between our two peoples".
In a wide-ranging speech, the President raised concerns in relation to climate change, the challenge of migration and the dangers posed by the growth of "individualism without social responsibility".
He expressed solidarity with Cyprus, as another island nation, and reaffirmed both countries shared commitment to the essential European values:
"While we may be at the geographical fringes of Europe, we are both now at the heart of the European discourse. Our respective national experiences afford us a unique perspective on the Union and enable us to make incisive and informed contributions regarding the possible futures of the European Union".
Referring to military intervention by Turkey in northern Syria President Higgins urged Turkey to cease attacks: "I call on Turkey to seek an alternative, negotiated approach, one that rejects military intervention and its resulting humanitarian distress, and one that rejects the coercion or forced returns of refugees".
President Higgns was also critical of recent drilling activities and gas exploration by Turkey off the coast of Cyprus:
"Today, I reiterate Ireland's view that matters of the maritime, and activities at sea, should be undertaken within the framework of international law and any argument on these matters should be settled through negotiations undertaken in that context".
The President thanked other EU member states for the support and solidarity displayed towards Ireland in the face of Brexit and said that the potential of a hard border on the island of Ireland could put the hard-won gains and progress of the Good Friday Agreement at risk.
President Higgins criticised recent threats to cut off aid funding to countries who failed to stem "unauthorised migration" and he called for a global response to address the migration crisis.
"Aid should not just focus on the areas where people are fleeing. It also must be directed at places where people are staying, either voluntarily or involuntarily, and shore up relevant institutions," he said.
"We need a global fund to anticipate, manage and respond to global migration with regional instruments with capacity to anticipate and respond."