Initial jobless claims fell again last week, and the private sector added 157,000 jobs in June, indicating potential strengthening in the jobs market. The Labor Department said the seasonally adjusted figure of initial claims for the week ended July 2 decreased by 14,000 to 418,000 from an upwardly revised 432,000 the previous week. Analysts surveyed by Econoday expected 420,000 new jobless claims last week with a range of estimates between 405,000 and 435,000. Most economists believe weekly claims lower than 400,000 indicate the economy is expanding and jobs growth is strengthening. Also Thursday, Automatic Data Processing Inc. said private-sector employment rose by 157,000 in June, well ahead of analysts’ estimates. Briefing.com expected 50,000 new private-sector jobs in June. Paul Ashworth, chief U.S. economist at Capital Economics, said June’s gain was double consensus projections of 70,000. “The bigger than expected 157,000 increase in June’s ADP payroll survey measure of private employment suggests that the U.S. economy started to recover some of the momentum lost over the preceding couple of months,” Ashworth said. The payroll giant conducts the monthly survey, which excludes federal jobs, in conjunction with Macroeconomic Advisers. The companies revised the May increase in nonfarm private-sector jobs downward slightly to 36,000 from 38,000. “This month’s jobs figures are a significant improvement over May’s, particularly in light of last quarter’s disappointing 1.9% GDP growth,” ADP Chief Executive Gary Butler said. “Given such strong employment results despite poor GDP, I am optimistic we will see improving job growth in the second half of the year.” The Labor Department said the four-week moving average of jobless claims, which is considered a less volatile indicator than weekly claims, fell to 424,750 last week from a slightly revised 427,750 the prior week. The total number of people receiving some sort of federal unemployment benefits for the week ended June 18 fell to 7.46 million from 7.51 million the prior week. The Labor Department reports nonfarm payroll data for June on Friday. On Wednesday, research firm Challenger, Gray & Christmas said the number of planned layoffs grew 11.6% in June even as job cuts fell to an 11-year low in the first half of 2011. Write to Jason Philyaw. Follow him on Twitter @jrphilyaw.