President Michael D Higgins discussed human rights with Cuban President Raúl Castro during the first day of his State visit.
The talks, which lasted nearly four hours, also involved LGBT rights and the status of non-governmental organisations, issues which are the subject of a Political Dialogue and Cooperation Agreement agreed between the EU and Cuba.
Other issues discussed included the Colombian peace process, according to a spokesperson for President Higgins.
Earlier, the President laid a wreath at the José Martí monument in what was the first visit to Cuba by an Irish head of State.
The aim of the visit is to provide an opportunity to build on what is regarded as a very positive relationship between Ireland and Cuba.
President Higgins is the first European head of state to visit Cuba since the signing of the agreement with the EU last December.
The Cuban government is understood to see the visit in the context of the wider EU-Cuba relationship as well as a bilateral relationship with Ireland.
Ireland's trade with Cuba has seen a large increase in percentage terms in recent years, but is still relatively small, totalling about €6m a year.