Business confidence shot up among Massachusetts employers last month and hit a level not seen since the early days of the new millennium, but a tight labor market still poses a concern.

The Associated Industries of Massachusetts Business Confidence Index jumped 2.4 percentage points to 66.6 in May, the business-backed association announced Tuesday. The index reading is 5.8 points higher than it was a year ago, AIM said, and employer confidence levels remain “comfortably within the optimistic range.” AIM said the last time the index was as high as 66.6 was in the summer of 2000.

AIM said the only “whiff of concern” in last month’s report came from the index that measures hiring, which dropped 1.5 points in May and has fallen 0.2 points during the year. The group attributed the declines to “the persistent shortage of workers in Massachusetts that has forced some employers to postpone expansions or to decline new business opportunities.”

“Massachusetts employers remain confident, but economic growth in the commonwealth is increasingly bumping up against the structural shortage of skilled workers,” economist and Northeastern University professor Alan Clayton-Matthews said. He told MassBenchmarks earlier this year: “Retiring baby boomers will continue to dampen labor force growth this year and throughout the next decade unless the commonwealth is able to attract young workers from across the country and the world.”

AIM’s index has been issued monthly since July 1991. It is presented on a 100-point scale, with 50 being neutral. The all-time high of 68.5 was recorded in both 1997 and 1998, the group said, and its low was 33.3 in February 2009. The index has remained above 50 since October 2013.