"Civil union is not the same as a marriage, there are so many limitations and it's time to change that," Ms Kennedy said.
Legalise Love president Joseph Hubgood said most people he spoke to were not aware that gay couples could not marry or adopt children.
"The biggest response we've had so far is not against gay marriage, it is utter shock that we don't already have it.
"We want to put this on the political agenda, so that people are aware of the issue," Mr Hubgood told APNZ.
Announcing its "rainbow issues" policy this week, Labour said it would legalise adoption for gay and lesbian people, which Mr Hubgood said was a good sign.
"We do have allies within most parties, people who agree with the issue," he said.
"It's always going to be controversial, if it wasn't then it would already have been done, but at the same time the global movement has never been as strong as it has been in this last year. It's now a matter of when, not if."
One man, Robert, said he had attended the rally to support friends who suffered from unequal rights.
"We're marching for the right for everybody to marry who they love and just who society says is normal for them to love," he said.
"I have the right to marry who I love but my best friend doesn't, so I'm here on the march to support."
The group's protest coincided with the United States' Spirit Day, a day for acknowledging people who have committed suicide as a result of homophobia in schools.