For the first time in six years, the share of U.S. workers offered health insurance through their employer has risen, a sign a tighter labor market is prompting businesses to offer more generous benefits.

In March, 69% of private-sector employees were offered medical benefits from their employer, according to an annual survey the Labor Department released Friday. That’s up from 67% in 2017, and the first time the rate has increased since 2012.

The...