MINNEAPOLIS — State health officials say a handful of Minnesota counties with low COVID-19 vaccination rates have slightly higher cases of the coronavirus.

Among the 10 counties with COVID-19 rates of 5 per 10,000 people or higher in the week ending June 5, none had vaccination rates that were above the state average.

The figures have Gov. Tim Walz concerned that some regions could be breeding grounds for more infectious variants of the coronavirus.

“We still have pockets of relatively low vaccination rates in parts of the state and country,” he said recently during a public appearance to promote vaccination. “Those pockets are starting to see an increase in some of those variants that showed up in India and some of those places.”

After having one of the nation’s highest rates for coronavirus cases this spring, the state now has the 24th lowest infection rate among states for the week ending June 10, the Star Tribune reported.

Minnesota reported four COVID-19 deaths Thursday and 142 infections. Those numbers raised the state’s totals in the pandemic to 7,527 deaths and about 604,000 infections, but reflected a decline in pandemic activity.