Charles, the heir to the British throne, shook hands with Adams, the veteran president of Sinn Fein, the political wing of the now-defunct Irish Republican Army paramilitary group.
The prince, 66, met Adams at the National University of Ireland's campus in Galway on the west coast, shortly after starting a two-day visit to the republic.
Adams leaned forward several times as they spoke for less than a minute, before introducing Charles to other guests.
Soldiers from the regiment were found responsible for several killings during the 1972 Bloody Sunday massacre -- one of the worst atrocities in the Northern Ireland conflict, known as "The Troubles."
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"But he (Charles) also has been bereaved by the actions of republicans," Adams said.
"Thankfully the conflict is over. But there remains unresolved injustices. These must be rectified and a healing process developed."
Adams has always rejected allegations that he was a key figure in the IRA, which killed Charles's beloved great-uncle and mentor Earl Mountbatten in 1979.
The 79-year-old, who was the last viceroy of India and a father figure to Charles, was killed along with two relatives, and Paul Maxwell, a 14-year-old local boy who worked on the fishing boat.
Charles was expected to travel yesterday to the rugged stretch of coastline near where the killing took place in Mullaghmore, becoming the first royal to do so on a visit that palace aides have said is aimed at promoting "peace and reconciliation".
Mountbatten's grandson, Timothy Knatchbull, who survived the blast, is also expected to attend, along with Peter McHugh, a local resident who helped pull bodies from the sea, British media reported.
Adams and other senior Sinn Fein members boycotted Queen Elizabeth II's groundbreaking visit to Ireland in 2011, the first by a British monarch since the future Republic of Ireland gained independence from Britain in 1922.
But Northern Ireland's Deputy First Minister Martin McGuinness, a member of Sinn Fein who was an IRA commander in the 1970s, later shook hands with the queen during her visit to Belfast in 2012 -- a historic meeting.