PROVIDENCE – Rhode Island regained the unfortunate distinction of having the second-highest state unemployment rate in the nation last month, the U.S. Labor Department said today.

Only Michigan, with an unemployment rate of 15.2 percent, had higher joblessness in June than Rhode Island, where the rate rose to 12.4 percent from 12.1 percent in May, the department’s Bureau of Labor Statistics said.

Close behind Rhode Island were Oregon (12.2 percent), South Carolina (12.1 percent), and Nevada (12 percent). In all, 12 states and Washington, D.C., had “significantly higher jobless rates than the U.S. figure of 9.5 percent,” the agency reported.

Sixteen of the 50 states now have double-digit unemployment rates, up from 13 in May. Rhode Island was the only state north of North Carolina or east of Ohio with unemployment above the U.S. rate of 9.5 percent in June. In fact, the Northeast has the lowest regional jobless rate in the nation at 8.6 percent, making Rhode Island even more of an outlier.

Thirty-eight states and Washington, D.C., saw unemployment rise in June, while seven states had no change and five states had a decrease in joblessness, the agency said.

The unemployment rate was 8.6 percent in Massachusetts and 8.0 percent in Connecticut, both below the national average.

Unemployment rose on an annual basis in every state and Washington, D.C., in June compared with a year earlier.

“No region of the U.S. is immune to the job destruction that’s going on,” Rebecca Braeu, an economist at John Hancock Financial Services in Boston, told Bloomberg News. “The rising unemployment rate is clearly going to hurt consumption. It’ll limit the recovery.”

In a small bit of good news, Rhode Island was not among the states with the highest month-over-month or year-over-year percentage decreases in employment.

Last month, Michigan became the first state to hit an unemployment rate of 15 percent or higher in a quarter-century, the last being West Virginia in March 1984.