A record 384,000 people filed initial claims for unemployment in Michigan last week amid continued punishing economic consequences of the coronavirus pandemic.

More than 800,000 sought jobless benefits over the past three weeks, according to figures released Thursday. The state’s 3.6% unemployment rate could top 15% when the April employment report is released in early May.

The state has been overwhelmed by a flood of applications, and some of those out of work have had trouble applying online or by phone. The Unemployment Insurance Agency is adding staff and expanding call center hours.