At the same spot on Monday evening, six masked men formed a guard of honour with one shooting a semi-automatic weapon into the air.
Yesterday, McElkerney's coffin was draped in an Irish tricolour and a starry plough flag before the masked group marched as part of the cortege towards St Peter's Cathedral.
PSNI superintendent Lorraine Dobson said: "Police had a proportionate operation in place which included the use of evidence gathering equipment.
"All evidence will now be reviewed by specialist officers and any offences detected will be investigated."
Among those attending the service were the Sinn Fein MLAs Caral Ni Chuilin and Gerry Kelly, whose wife Margaret is the sister of McElkerney.
The 56-year-old died last Friday - a day after he was found with a gunshot wound at the republican plot in Milltown Cemetery.
He was jailed in 1987 for his role in a 1982 booby trap-bomb at Divis Flats.
The INLA bombing killed two schoolboys, Kevin Valliday (11) and his friend Stephen Bennet (14), as well as 20-year-old Lance Bombardier Kevin Waller.
He was later identified in court as acting as the lookout for the terrorist who triggered the device.
McElkerney received three life sentences, however he was later released under the terms of the Good Friday Agreement in 1999.
As Fr Gary Donegan led the funeral service yesterday, the masked men waited in an alleyway outside as a surveillance plane circled above.
Fr Donegan said: "There are tragedies in life that we can do nothing about.
"Martin's death is such a tragedy."
One of 13 siblings, McElkerney was born off the Crumlin Road in north Belfast on June 27, 1962.
Fr Donegan added: "The family were burnt out of their home in north Belfast early on in the Troubles, and they got passports stamped as they crossed the border from north Belfast to 'Disneyland' in west Belfast.
"This was a very different experience for the McElkerney family.
"They left behind the comfort of the small streets around the Crumlin Road to move into two caravans in Beechmount, before eventually settling in Springhill, or Beirut as it was known at the time."
He noted that the former prisoner's first work placement in his job as a painter and decorator had also been in St Peter's Cathedral.
The family had told the priest that the loss of many friends during the Troubles had a profound influence on Martin's decision to get directly involved in the conflict.
"Those were sad and difficult times.
"They 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," he added.
Fr Donegan claimed that after McElkerney was released from prison he later "became aware that the choices he made in life had significant and lasting consequences for others, including his family".
In yesterday's Irish News, there were more than 150 individual funeral notices placed for McElkerney.
They included messages from his wife Ann, his children and wider family.
Following the service the masked men again stood in formation outside the cathedral to carry his coffin.
A funeral notice had originally said the burial was scheduled to take place in Roselawn Cemetery but instead it proceeded to Milltown Cemetery.