MINNEAPOLIS — Gov. Mark Dayton told leaders of Minnesota’s counties Monday that he’s sympathetic to their financial difficulties, but promised no immediate relief.

Dayton was speaking at the annual convention of the Association of Minnesota Counties. He predicted “big property tax increases this year and next” as counties struggle to make up for declines in state aid programs even as property owners contend with the elimination of the homestead market value credit — a popular program that reduced most peoples’ property tax bills.

Dayton called property taxes “the most unfair tax of all — you have to pay it whether or not you have a job or an income.” The Democratic governor said he’d like to lessen pressure on property taxpayers with income taxes that take more from wealthier earners — but said he wasn’t likely to make another big push for those changes until at least 2013, after the next legislative election.

It’s an understandable strategy for Dayton, who’s found Republican legislative leaders highly unreceptive to his proposed income tax hike on the wealthy. But county commissioners at Monday’s meeting in downtown Minneapolis said their budgets are quickly stretching to the breaking point.

“We’re running on the bare bones,” said Rachel Nystrom, a Crow Wing County commissioner from Baxter, near Brainerd. Nystrom said she and fellow commissioners managed to reduce their property tax levy the last three years in anticipation of state aid cuts — but that most property owners in the area will still see higher property tax bills this week, thanks to the elimination of the homestead credit.