The Taoiseach has said that he has expressed the Irish Government's "annoyance and anger" at the slow pace of the justice system in dealing with those responsible for the death of Private Seán Rooney.
Private Rooney died when the vehicle he was travelling in came under fire on the way to Beirut in December 2022.
Last July, six people were convicted of involvement in the killing, with most receiving lenient sentences.
The main defendant, Mohammad Ayyad, was sentenced to death, but he has still not been detained and remains at large.
Speaking following a meeting with the Lebanese Prime Minister, Taoiseach Micheál Martin said he insisted that there must be accountability.
"Accountability means that the people responsible for the death of Sean Rooney are brought to justice, proper justice, the sentencing was extremely lenient and the people are at large."
The two leaders also spoke about an attack on Irish peacekeepers two weeks ago, during which a patrol involving Irish peacekeepers came under attack in the Irish area of operations.
Mr Martin said the commander and the patrol dealt with the attack professionally, and in this case the Lebanese government arrested a number of suspects quickly.
They will now go through the criminal justice system.
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The UNIFIL mission in South Lebanon, which involves more than 360 Irish soldiers, is due to come to an end in December next year when the UN mandate ends after 48 years.
The Taoiseach said he believes that there may be a continuing role in peace monitoring and training mission for Irish troops in South Lebanon.
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The UNIFIL mission monitors activity, supports the local population and assists the Lebanese armed forces.
Part of their mission includes holding ground and monitoring incursions across the Blue Line - which is the de-facto border between Israel and Lebanon.
Since last year, when Israel invaded Lebanon, the Israeli Defence Forces have maintained a presence in Lebanon, including a position on high ground close to an Irish manned outpost on the Blue Line.
The future for Lebanon after next December remains highly uncertain, with many fearing that Israel and the Iranian backed Lebanon militia force Hezbollah could resume hostilities.
Taoiseach intends to lead FF into the next election
The Taoiseach also said it is still his intention to lead his party into the next election, and he has rejected suggestions from his critics that he has "lost the dressing room".
Speaking in South Lebanon, Mr Martin said: "TDs and senators are saying to me keep doing what you're doing as Taoiseach in terms of focusing on the core issues facing the Irish people."
Asked if he intended to lead the party into the next election, he said "yes".
When a question was put to him about comments from a Fianna Fáil backbencher that he had "lost the dressing room", the Fianna Fáil leader said: "I have a lot of experience of dressing rooms throughout my life, in Cork as well, and I know how to keep a dressing room".
