A relationships register that recognises unmarried couples, opposite-sex and same-sex, has been described as an insult, with one Sydney Liberal saying it puts some relationships on the same level "as cats, dogs and cars".

City of Sydney Liberal councillor Shayne Mallard said politicians were too scared to approach civil unions or gay marriage despite several countries doing so and public support.

Cr Mallard, who has been in a same-sex relationship for a number of years, said the register was a step forward but ultimately an insult.

"My partner is Danish, and over in Denmark they are far more advanced and even have same-sex adoption laws," he said.

"I would need to talk to my partner about whether we would want to register but I imagine he would not want to be registered as he would not be keen to be part of a second-best system.