Forum chairman Wayne Walker said the move was the most efficient and economic way of reducing the the amount of airborne particles that could cause lung problems.
"It still needs to be ratified, but I really hope it goes through. We don't think we've got a lot of choice. We need to be moving on this.
"There are other cities in New Zealand that have already applied the point-of-sale with some good effect and I thought it was quite a reasonable option."
Mr Walker said transport and industry were also responsible for a lot of particle emissions, but domestic heating was the area in which the council could have a direct influence.
"Transport is difficult because we're very reliant on the Government to bring in more stringent controls on emissions, such as tighter controls on vehicles."
There are already some restrictions on open fires in new Auckland homes, but the forum said that without stricter rules, emissions targets would not be met until 2042.
If the council agreed with the recommendations in the paper, an open fire ban would begin in 2014 and point-of-sale rules in 2015.
The new bylaw would bring Auckland into line with other regions such as Nelson, which has banned open fires and is phasing out enclosed burners.
A report published last year by the council showed that domestic heating, transport and industry emitted 18.4 tonnes a day of particles on a typical winter day.
Open fires and solid fuel burners contributed 13 tonnes of this total.
The cost of air pollution in urban areas was believed to be at least $727 million a year.
The report's authors reckoned air pollution was responsible for 737 premature deaths a year, and illness caused by dirty air prompted Aucklanders to take 1.16 million sick days a year.
The forum was also looking to expand a $3 million programme which provided financial assistance and advice for people to retrofit their homes with cleaner heat and insulation.
More than 900 people have applied for the incentive, which gave homeowners up to $5000 of assistance, paid back through targeted rates.