New signs of weakness in private sector job growth and in the economy sent stocks tumbling yesterday for the third straight day to wreck Wall Street’s recent rally — and continue concern over the fragile recovery.

A report from payroll firm Automatic Data Processing said employers added just 179,000 to their payrolls in April, well below the 198,000 expected by Wall Street. The pre-market announcement sent stocks tumbling at the open — a drop they could not recover from.

The drop raised fears that tomorrow’s monthly jobs report from the Labor Department would also be weak, confirming that the pace of recovery is indeed slowing.

Economists expect the government report will show 185,000 jobs were added in April, after 192,000 were added in February and 216,000 were added in March.

Meanwhile, employers have slowed their pace of laying off workers, said consulting firm Challenger, Gray & Christmas. The firm said announced layoffs last month dropped 12 percent to 36,490 compared to 41,528 in March.

Separately, a report on the services industry from the Institute for Supply Management said non-manufacturing activity slowed noticeably in April. Its index dropped to 52.8 from 57.3 in March, with new orders at the lowest level since December 2009.

“This is a sector that is supposed to be relatively smooth in terms of growth, so if it turns out to be more than transitory, this would be a clear indication of de-stabilization in the economy.” said economist Pierre Ellis at Decision Economics.

After falling sharply at the opening, the Dow Jones industrial average recovered to end the day 83.93 lower, at 12,723.58. The Standard & Poor’s 500 Index lost 9.30, to 1,347.32. The Nasdaq fell 13.39 to 2,828.23.

“I think there is a chance that we put the high in for the year,” said bearish portfolio manager Doug Kass at Seabreeze Partners Management.

At the same time, the dollar fell to a new three-year low against major currencies, while the average gas pump price in the US was just two cents shy of $4 a gallon. In the past month, a gallon of regular has jumped 32 cents. tharp@nypost.com