ST. PAUL — Recent flooding across Minnesota has caused at least $32 million in public infrastructure damage, state leaders said Tuesday while warning that the total is likely to rise.

Gov. Mark Dayton and his emergency managers provided the estimate as the Federal Emergency Management Agency dispatched teams to survey the fallout from sustained rains that led to overflowing lakes and rivers. The state officials said the early tally makes them confident that Minnesota will be eligible for federal assistance to offset costs of response and recovery. Flooding damage was seen in nearly half of Minnesota’s counties.

As the federal team headed to four southern counties, state emergency management director Kris Eide said two northern counties “still are in the flood fight” and keeping eyes on Rainy Lake and Lake of the Woods, which have yet to crest.

Carver County, situated southwest of the Twin Cities, has turned in the biggest damage total so far at $9.2 million because of severe problems with roads and a wastewater treatment plant. In St. Paul, the Mississippi River was finally receding after swallowing up downtown access roads and an island park. The high waters already forced the relocation of a major city food festival and the annual Fourth of July Fireworks display.

The state has a $3 million relief fund to help match federal disaster aid. Dayton hasn’t ruled out calling a special legislative session if the state account is tapped out, but said it was premature to decide on that.