Health Minister Tony Ryall said British American Tobacco was "wasting its money" on the campaign.
New Zealanders were turning against tobacco companies and their marketing strategies, he said.
"New Zealanders have moved on from being influenced in this way. There is a lot of support for what the Government is doing in tobacco."
The campaign's cost, which would be "hundreds of thousands of dollars", was "small" compared to the intellectual property that needed protecting, Mr Rush said.
"To remove the rights of a legal company to use its own branding, branding that it has created and invested in, has far wider repercussions than just tobacco," he said.
Mr Rush said it set a "disturbing precedent" for other industries, saying the British Government was considering a similar proposal for alcohol.
The push by British American Tobacco comes one week after the landmark decision by the High Court of Australia to uphold its government's Plain Packaging Act.
Mr Rush said New Zealand should not "blindly follow Australia's lead" with policy he said was unproven in helping curb smoking.
The World Health Organisation has applauded Australia's legislation, saying it "sets a new global standard for the control of a product that accounts for nearly six million deaths each year".
Action on Smoking and Health spokesman Michael Colhoun said British American Tobacco's argument that plain packaging would fail to reduce smoking while jeopardising their revenue was "having a dollar each way".
"You can't argue for both sides and go away with any credibility," he said.
Mr Ryall said the Government would keep an eye on the campaign to make sure it was not breaking laws banning the advertising of tobacco.
Mr Rush announced the campaign in front of posters with the slogan: "We agree that tobacco is harmful. We disagree that plain packaging will work."
The company has also launched the website agreedisagree.co.nz.
- additional reporting, Isaac Davison of the New Zealand Herald
