15 October 2015 Last updated at 19:07 BST
Garda Anthony Golden, 36, was killed as he responded to a woman's complaint of domestic abuse in Omeath, County Louth, on Sunday.
Politicians and senior police officers from both sides of the Irish border attended the church ceremony in Blackrock, County Louth, where Garda Golden lived with his wife and three children.
Thousands of mourners who lined the streets heard his brother and the head of Irish police, Garda Commissioner NÃ³irÃ­n O'Sullivan, pay tribute to his bravery.
BBC News NI's Dublin correspondent Shane Harrison reports.
An Irish policeman who was shot dead on duty in the Republic of Ireland has been hailed as a hero at his state funeral.