(Adds context on split within Fed, unemployment claims)
By Jonathan Spicer and Stephanie Kelly
NEW YORK, Aug 18 (Reuters) - Strong employment and a long-awaited return of middle-wage jobs suggest the labor market is tightening and the broader U.S. economy is on track, an influential Federal Reserve policymaker said on Thursday, appearing to reinforce his more confident message on a possible interest-rate hike.
New York Fed President William Dudley, a permanent voter on U.S. interest-rate policy and a close ally of Fed Chair Janet Yellen, said the last two months of employment "helped allay concerns that arose earlier this year that job growth was beginning to stall (and) reinforced my view that labor market conditions continue to improve."
While Dudley had some cautionary words on Puerto Rico's struggling economy, he painted a relatively bright picture of the national labor market that prompted investors to send Treasury yields somewhat lower and, briefly, to boost the dollar.
The comments come as investors struggle to parse mixed messages on whether a rate hike is imminent. Minutes from the Fed's July policy meeting show Dudley's colleagues are torn between hiking soon based on labor market strength, or waiting until inflation is more evident.
Earlier this week, Dudley said rates could possibly rise as soon as September, depending on the economic data and signs of inflation.
"The labor market continues to tighten," he said on Thursday, citing evidence of wage gains in the employment cost index and in average hourly earnings, two key pieces of data. The roughly 2.5 percent growth in wages "suggests we are getting closer to full employment."
In another sign of labor resilience, data on Thursday showed the number of Americans filing for unemployment benefits dropped more than expected last week.
Meanwhile, the U.S. economy appears to be bouncing back from a weak growth rate of about 1 percent in the first half of the year. That, along with overseas risks and financial market volatility, caused the Fed to stand pat on policy since hiking rates from near zero back in December.
While Dudley said he expects growth to reach about 2.5 to 3 percent in the second half of the year, he said the labor market would factor more in his rate-hike decision in part because U.S. productivity remains a wildcard. "At the end of the day, how the GDP growth translates in terms of employment gains is probably the more important element," he said.
Investors give about an 18 percent chance of a Fed rate hike next month, and almost even odds of a move in December after the November U.S. presidential election.
Citing fresh New York Fed research on the "hollowing out" of the labor market, in which positions like teachers and mechanics have faded in the last few decades and contributed to American 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.
And turning to Puerto Rico, which lies in the New York Fed's district, Dudley said reforms, a debt-burden adjustment, and economic growth were all needed to tackle its "unsustainable" public debt.
Reporting by Jonathan Spicer and Stephanie Kelly; Editing by Chizu Nomiyama and Alan Crosby