The taoiseach (Irish prime minister) says he believes the EU will respond positively if the new UK prime minister shows they want to reach an agreement on the Northern Ireland Protocol.
Micheál Martin said he wanted to work with Boris Johnson's successor in an open and constructive way.
The EU chief Brexit negotiator has urged the new prime minister to engage in talks.
A new Conservative Party leader and prime minister is expected on Monday.
Speaking to the British-Irish Association conference in Oxford, Mr Martin said Brexit marked a fundamental change in the relationship between the EU and the UK.
Mr Martin said he was deeply concerned by UK government legislation which would give ministers the power to scrap parts of the protocol – the post-Brexit deal between the UK and the EU.
"Regrettably, unilateral action on the protocol and on legacy is at odds with the spirit of partnership that is needed to underpin the Good Friday Agreement," he said, referring to the 1998 peace deal which ended the worst of more than three decades of violence in Northern Ireland.
Mr Martin said he wished the new prime minister well.
"I want to work in an open and constructive way with the new British prime minister," he added.
"I sincerely believe that the EU would respond positively to a serious and genuine signal from the new British prime minister that their priority is to reach an agreed outcome on the issues around implementation of the protocol."
The Northern Ireland Protocol is a special arrangement that keeps Northern Ireland in the EU's single market for goods, avoiding a hard border with the Republic of Ireland.
The arrangement ensured free trade could continue across the Irish land border, which is a sensitive issue because of the history of conflict in Northern Ireland.
But the protocol brought in some new checks on goods moving between Great Britain and Northern Ireland and has been criticised by unionist politicians.
However, the majority of politicians elected to the Northern Ireland Assembly in May's elections support the arrangements.
The UK signed up to the protocol as part of the agreement which took the UK out of the EU.
It now wants changes to the deal, including fewer checks on goods travelling between Great Britain and Northern Ireland and for any trade disputes to be resolved by "independent arbitration" and not by the European Court of Justice.
The EU has said a way forward could be found by further exploring the commission's proposals for reforming the post-Brexit treaty.
The bloc has warned the UK against taking unilateral action.
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