The Centre Party wanted to restrict advertising of product information while the conservative National Coalition Party wanted to intervene on certain marketing methods.
Government parties did not agree on how any restrictions would be enforced, either.
Social Services Minister Paula Risikko said that the matter would come up again in negotiations over the formation of a new government following the General Election in April.
Risikko does not believe the preparatory work will go to waste, because there is now a solid foundation should the issue become live again in the next parliamentary term.
Centre party MP Paula Sihto, who participated in the negotiations, said that the restrictions could go even further, and involve a total ban on alcohol advertising.
Risikko would not comment on that suggestion.
Alcohol sales are restricted in Finland. A government monopoly, Alko, is the only enterprise licensed for retail sales of alcohol stronger than 4.7 percent.