New applications for unemployment insurance benefits dropped 18,000 to 214,000 in the first week of July, the Department of Labor reported Thursday.

Forecasters had expected around 225,000 new jobless claims. Instead, they fell more than expected to the lowest since May, when claims were plumbing the lowest levels since the 1970s.

[Also read: Inflation edges up to 2.9 percent in June, highest in six years]

Low claims are a good sign. They suggest that layoffs are rare and that job creation is high.

The claims data for recent months show no signs that the unemployment rate, at a decades-low 3.8 percent, is heading back up. In fact, they indicate it has room to fall further.

Thursday's release signals "more than enough strength in employment growth to keep the unemployment rate trending down," noted Jim O'Sullivan, chief U.S. economist for High Frequency Economics.

Economists calculate that any number of claims below around 300,000 means that unemployment will stay steady or fall. Claims haven't hit that mark since early 2015.

After months of very low new claims for benefits, the total number of people receiving unemployment insurance has dwindled. Altogether, just 1.74 million people are receiving benefits, which are available for up to 26 weeks in most states. That is a number not seen before this late spring since the winter of 1973.