Strong recent U.S. jobs growth and a long-awaited return of middle-wage employment are two positive signs for the U.S. labor market, an influential Federal Reserve policymaker said on Thursday, reinforcing his positive message on the broader economy.

New York Fed President William Dudley said the last two months of job growth "helped allay concerns that arose earlier this year that job growth was beginning to stall. Indeed, these reports reinforce my view that labor market conditions continue to improve," he said in prepared remarks to a press conference.

Turning to fresh New York Fed research on the "hollowing out" of the labor market, in which positions like teachers and mechanics have faded in recent years and contributed to wage inequality, Dudley said "the tide has begun to turn."

"For the first time in quite a while, gains in middle-wage jobs actually outnumber gains in higher- and lower-wage jobs nationwide," said Dudley, a permanent voter on U.S. interest rate policy and a close ally of Fed Chair Janet Yellen.

"I believe this is an important development in the economy, because, if it were to continue, it would create more opportunities for workers and their families who have been struggling up to now."

The policymaker said earlier this week the Fed could possibly raise rates in September. He did not comment on rates in the prepared remarks on Thursday.