WASHINGTON -- Even as hiring remains mediocre, at least workers can take heart in this: Employers are holding on more tightly to their existing staff. In the latest sign of diminishing layoffs, the number of workers applying for new unemployment benefits fell last week to the lowest level in nearly six years, the U.S. Labor Department reported Thursday. For the week ended Saturday, 320,000 workers filed first-time jobless claims. That was a drop of 15,000 from the prior week and the lowest batch of initial filings since the first week of October in 2007, just a couple of months before the start of the Great Recession. Unemployment claims have been sliding in recent weeks, an encouraging sign for a job market that showed signs of weakening in July. Last month, the pace of job growth slowed to 162,000 net new hires, compared to 188,000 in June. What's more, the data suggest many of the new jobs in recent months have come in lower-wage industries that offer fewer hours of work. The sluggish hiring makes things hard for the 11.5 million officially unemployed and another 8.2 million part-time workers who want more hours. Still, the drop in jobless claims means that people who have jobs may feel a little more secure, as many companies already have cut to the bone and are operating very tightly. The latest weekly report surprised analysts, many of whom were expecting a slight increase from the prior week. Unemployment filings vacillate from week to week, and the data can be tricky to read, especially during the summer because of temporary auto plant shutdowns. Even so, the more reliable four-week moving average of initial claims also has been drifting lower. For the four weeks ended Aug. 10, the average dropped to a new post-recession low of 332,000 from 336,000 in the prior four-week period. For the record, 4 p.m., Aug. 15: A previous version of this post said the pace of job growth last month slowed to 166,000 net new hires. The number is 162,000.