Orijol Rukaj was at the Keilor East cemetery, in Melbourne's northwest, on April 25 under the supervision of Corrections Victoria officers.
The 47-year-old was given permission to make the supervised visit while being held in remand at a correctional centre in Lara, northeast of Geelong.
He was set to face court in June on drug importation charges, Victoria Police Acting Inspector Simon Pengelly told reporters on Thursday.
"We don't believe that he's a danger to the community, but obviously they're very, very serious charges of drug importation," Act Insp Pengelly said.
Rukaj was tasked with carrying his brother's casket and was one of about 300 people who attended the ceremony, Victoria Police said.
At some point during the funeral, he managed to evade his supervisors and is believed to have fled the location in a dark coloured Land Cruiser.
"We believe that he was picked up by that Land Cruiser and left, but just due to the sheer amount of people, (they) couldn't see," Act Insp Pengelly said.
There have been no confirmed sightings of Rukaj, who police say has links to Albanian organised crime, in the intervening six weeks.
On Tuesday, police attended 20 addresses across Melbourne to inquire with Rukaj's associates as to his whereabouts.
Those inquiries led police to believe the fugitive remains in hiding in the Melbourne area.
Police have identified a number of people believed to have assisted Rukaj with his escape, but they are not currently in Australia.
One person police believe may have assisted him was arrested at Melbourne Airport on Thursday morning but was released without charge.
Police are continuing to make inquiries about that person, who is believed to have been travelling from Europe via the Emirates.
Part of those inquiries concern phone calls the pair are believed to have conducted while Rukaj was in prison.
Asked about the protections in place to prevent his escape, Act Insp Pengelly said it was a matter for Corrections Victoria.
"It's something that I don't have the knowledge in relation to what their protocols are," he said.
Opposition Leader Jess Wilson said prisoners should be under constant surveillance when released to attend a funeral.
"This is just a failure of the corrections system," she told reporters on Thursday.
"I guess in Victoria we can't put people into the corrections system in the first place and we actually can't keep them in the corrections system either."
Members of the public are urged to come forward with any sightings, but police say Rukaj is not considered violent.
Corrections Victoria has been contacted for comment.
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