Enda Kenny has asked David Cameron to visit Ireland for the commemorations of the 1916 Easter Rising against British rule.
The Taoiseach said his Downing Street counterpart would consider the invitation in due course “if that is appropriate”.
Speaking after their meeting at Number 10 in London, Mr Kenny said the pair had discussed the “comprehensive, inclusive, sensitive” centenary celebrations of the rebellion.
“I have invited the Prime Minister to come over himself at some time during the year, if that is appropriate, and obviously he will consider that in due course,” he said.
Mr Cameron acknowledged the anniversary of “important events in our shared history”.
“We’ll mark them, as we should, in a spirit of mutual respect, inclusiveness and friendship,” he added.
Government suggestions last year that a member of the Royal family could be invited to take part in the main State celebrations provoked an outcry.
The proposal was then binned and a decision taken that will see Dublin-based ambassadors as the only representatives of foreign governments asked to attend events on Easter weekend.
However, Dublin’s Heritage Minister Heather Humphreys has since hinted the Prince of Wales could be invited to some of the peripheral events.
Two weeks ago Mr Kenny declared his disappointment in Northern Ireland’s new First Minister Arlene Foster’s plans to snub commemorations.
The rising in Dublin was a seminal moment in Irish history which ultimately led to partition and the creation of both the Republic of Ireland and Northern Ireland.
Ms Foster denounced the event as an attack on the State and democracy which more recently, she said, gave ”succour” to violent republicans in Northern Ireland.
Throughout 2016, more than 40 State ceremonial events will be held as part of the Ireland 2016 Centenary Programme.
Oxford and Cambridge Universities are among major UK institutions marking the anniversary.
Centenary celebrations at London’s Royal Festival Hall, the Barbican Centre, as well as venues in Birmingham, Manchester, Glasgow, Cardiff and other cities are among more than 87 events in the UK throughout the year.