A large crowd of men with their faces covered and wearing berets led the funeral procession to the church.
His coffin was draped in the tricolour and the starry plough flag.
At McElkerney's funeral, family friend Fr Gary Donegan said that his family are in "confusion, bewilderment and grief" at his death.
Fr Donegan told those gathered that McElkerney had experienced "a good start in life".
"The family were burnt out of their home in north Belfast early on in the Troubles," Fr Donegan said.
He told mourners that the deaths of friends led McElkerney to join the INLA.
"According to his family, the loss of many friends in the conflict, had a profound influence on Martin’s decision to get directly involved in what is euphemistically referred to as ‘the Troubles,'" Fr Donegan said.
"Those were sad and difficult times, and are hardly recognisable 21 years after the Good Friday Agreement which saw Martin released from Long Kesh after a decade and a half of incarceration."
Fr Donegan said that McElkerney was aware of the impact of his actions during the Troubles.
"Following his release from prison, Martin became aware that the choices he made in life, had significant and lasting consequences for others, including his family," he said.
McElkerney (57) died last week after he was found with a gunshot wound at the republican plot in Milltown Cemetery.
On Monday evening masked men fired shots in west Belfast to mark McElkerney's death.
Video footage emerged on social media showing one man firing a rifle into the air outside a house, before retreating inside.
Triple killer McElkerney was jailed in 1987 for his part in a 1982 booby-trap bomb which killed two schoolboys, Kevin Valliday (11) and his friend Stephen Bennet (14), as well as 20-year-old Lance Bombardier Kevin Waller.
The INLA man had been identified in court as the lookout for the bomber who triggered the device at Divis Flats in 1982.
McElkerney received three life sentences in 1987, but was released in 1999 under the terms of the Good Friday Agreement.