Irish president Michael D Higgins, Tanaiste Leo Varadkar, Foreign Affairs Minister Simon Coveney, Justice Minister Helen McEntee, SDLP leader Colum Eastwood and a representative of the Taoiseach Micheal Martin were among those who attended the service at the Church of the Immaculate Conception in Allenwood, Co Kildare.
Tributes have been paid across Ireland to Mr Currie, one of the key figures in the civil rights movement in Northern Ireland who also helped to found the nationalist SDLP party and was elected to parliament on both sides of the Irish border.
Mr Currie’s daughter Estelle said he was a hero to so many.
“Wow daddy, 82 years young, what a force for change you have been, what a force for good,” she told mourners.
“There have been so many tributes paid since Tuesday – the finest, fearless, immense courage, a true giant of civil rights and constitutional politics, one of its founding fathers. Daddy was always a hero to us, now we know he was a hero to so many others too.”
Mr Currie, 82, died in his sleep at his home in Derrymullen, Co Kildare, on Tuesday.
He was born in Co Tyrone, the eldest of 11 children.
Another service will take place on Saturday morning at St Malachy’s Church in Edendork, Co Tyrone, before burial in the adjoining cemetery.
Mr Currie’s decision to squat at a council house in Caledon in June 1968 is widely seen as the beginning of the civil rights movement, which challenged inequality and discrimination against Catholics.
Ms Currie said her father was “so proud of his roots” in Co Tyrone.
She recalled her father’s struggle for civil rights, taking a stand over the allocation of housing, and how he was an “orator” with a distinctive voice and dramatic delivery at meetings, conferences and on the campaign trail.
“When he squatted in Caledon in June 1968, he felt such a strong sense of injustice. He felt that they’d tried everything else,” she said.
“The civil rights movement was the most successful political action in Ireland, and for daddy it was the defining moment.”
She recalled her father having to keep a gun beside his bed and check under his car before taking his children to school every morning.
“Daddy reached the great old age of 82 and he died peacefully in his own bed – if you’d said that to him at the age of 30, he would never have believed you,” she said.
“But he never stopped thinking about the people who didn’t, Columba McVeigh killed by the IRA in 1975 and still lying somewhere far away from home.
“At every occasion he could, daddy would call on the people who took Columba away, to do the decent thing, the Christian thing, of allowing him home to be buried with his family.
“The disappeared, still one of the cruellest and shameful atrocities of the Troubles and still something that could be put right.”
Mr Currie went on to create the SDLP along with John Hume and Gerry Fitt in 1970.
In 1989, he won a seat in Dublin West for Fine Gael and pursued a career as TD and minister in the Republic until he retired in 2002.