Tax would be applied after an asset is sold and on the gain in value between April 2021 and the sale price.
Tax Justice Aotearoa spokesman Paul Barber, who is a policy adviser for the NZ Council of Christian Social Services, said the group was not pushing for any specifics when it came to a CGT.
"We want to see greater fairness, transparency and equality in our tax system. At the moment we have nothing. Any capital gains tax would be step further.
"The Tax Working Group clearly showed that inequalities with income and wealth are too high. There is a big hole in our tax system because we have no capital gains tax.
"We're one of the few developed countries who do not have a capital gains tax. This is nothing new. It's nothing outlandish. It works really well in other parts of the world and could benefit us all by bringing billions of dollars in revenue to help run those essential services that make our country a good place to live."
He said a majority of New Zealanders wanted a CGT, but Taxpayers' Union executive director Jordan Williams said the opposite was true.
"It's a shame than more media turned up than supporters for the CGT," Williams said.
Williams questioned whether the group was using taxpayers' money for its campaign, which included about $15,000 spent on advertising in newspapers, bus shelters and billboards.
But Barber said it wasn't, and that he had made a mistake on Radio NZ this morning when he said a taxpayer-funded group was part of the campaign.
"There's no public money involved."
Campaign supporters include the Public Health Association, New Zealand Council of Christian Social Services, Council of Trade Unions, Public Service Association, Hui E! Community Aotearoa, Equality Network, Closing the Gap, Poverty Action Waikato, and UCAN (United Community Action Network).
The group has also launched a petition in support of a CGT, which had 389 signatures by 11.30am today.