Initial jobless claims in the past month hit their lowest level since the start of the Great Recession, indicating the labor market might be nearing a return to normal.

The number of people filing for first-time unemployment benefits rose slightly last week to 304,000 from the previous week’s upwardly revised figure of 302,000, the Labor Department said Thursday.

Despite the revision, the 302,000 claims in the week ended April 5 were the lowest since May 2007.

A more stable barometer — the four-week average of new claims — dropped to 312,000 last week. The Labor Department said that was the lowest since October 2007, two months before the start of the worst economic downturn since the Great Depression.

“Current labor market conditions are at full-employment levels,” said Chris Rupkey, chief financial economist at the Bank of Tokyo-Mitsubishi in New York. “Claims are back where they were before the recession began.”

Lindsey Piegza, chief economist at Sterne Agee, cautioned that falling jobless claims are only half of the labor market equation. While they indicate fewer layoffs, they don’t point to greater job creation.

She noted that “claims have been on the decline for quite some time, and that hasn’t yet translated into meaningful improvement on the other half of the equation, job creation, as hiring remains unimpressive.”

The economy added a solid 192,000 net new jobs in March, and economists are expecting the recovery to accelerate this spring after a slowdown over the winter attributed to severe weather.