The chief of the Navy has apologised for giving a sailor who murdered his ex-girlfriend a funeral with full military honours.

Key points: Kate Malonyay murdered by ex-boyfriend Elliott Coulson in 2013

Kate Malonyay murdered by ex-boyfriend Elliott Coulson in 2013 Coulson took own life, was given funeral with full military honours

Coulson took own life, was given funeral with full military honours More than 10,000 sign change.org petition calling for Navy apology

More than 10,000 sign change.org petition calling for Navy apology Chief of Navy says sorry, says funeral policy will be more closely scrutinised

In April 2013, Elliott Coulson strangled 32-year-old Kate Malonyay in her unit on Sydney's north shore, several months after she had ended their year-long relationship.

In the days after her death, Coulson used Ms Malonyay's mobile phone to impersonate her, texting her friends and family when they became worried about her.

He then fled to the Gold Coast, where he booked into the Marriott Hotel. When police stormed the hotel room Coulson took his life by jumping off the balcony.

Days later, the Australian Navy gave Coulson a funeral with full military honours.

Ms Malonyay's friend Melissa Meredith told the ABC's Hitting Home documentary of her shock at the military's involvement.

"Those kind of ceremonies are for heroes. This guy was not a hero," she said.

The documentary prompted Lauren Sams to start a change.org petition demanding that the chief of Navy, Vice Admiral Tim Barrett, apologise and donate the cost of the funeral to a domestic violence support group.

The petition has more than 10,000 signatures.

"I just became so angry that something that is meant to be saved for the very best people in our society — people who put their lives on the line, people who risk their lives, who go out of their way, who spend their lives helping other people — something that's usually reserved for them was wasted on someone who represents the very worst in society," Ms Sams told Lateline.

Vice Admiral Barrett has since issued a statement saying sorry.

"I was, and remain, appalled at the brutal and violent murder at the hands of Elliott Coulson and I utterly condemn the abuse and violence that ended in her tragic death," he said.

"I acknowledge that the decision to support Elliott Coulson's family with Navy participation in the funeral has caused distress to Ms Malonyay's family, friends and the wider community.

"It was not Navy's intent to cause this distress and for this, I unreservedly apologise."

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Vice Admiral Barrett said in future there would be closer scrutiny of the Navy's funeral policy.

He said the Navy had received accreditation through the White Ribbon Organisation and had been providing training and education programs to its members.

Ms Sams said members of the military had expressed their disgust over Coulson's funeral in the petition's comments section.

"People on the petition who are saying 'this is not what military funerals are for. This is an outrage, I condemn this as members of the military'," she said.

"I guess that is probably the most gratifying thing, that people from that field and that area are saying 'this does not represent me. I don't stand for this'."

Ms Sams said she welcomed Vice Admiral Barrett's apology.

Ms Malonyay's friends and her mother Wendy told the ABC's Hitting Home that Coulson had been controlling and they were concerned he was stalking Kate after they broke-up.

Wendy Malonyay said they wish they had taken action against him.

"Any of these subtle signs, for God's sakes just go to the police. Don't just sit there and wait for what happened to my daughter. Because it's horrific," she said.

She said she is still haunted by her daughter's violent death at the hands of Coulson.

"He stayed in the unit for two days with her [after her death]. That horrifies me. It haunts me to know that she was in that unit for five days, dead," she said.