By Howard Schneider

WASHINGTON A new U.S. employment report on Friday will show whether the labor market continued to moderate through September in what could be an important waypoint for Federal Reserve officials deciding whether to push ahead with another interest rate increase this year or sit tight.

The report will be released at 8:30 a.m. (1230 GMT), based on surveys conducted before a United Auto Workers strike could influence the outcome.

Economists polled by Reuters expect the economy to have added another 170,000 positions in September, modestly above the 150,000 pace of the last three months, with the unemployment rate falling slightly to 3.7% from 3.8%.

Coupled with an unexpected jump in job openings in August, that is the sort of outcome that could leave the immediate policy debate unresolved for now given an economy that continues to surprise with above-trend growth even as economists expect at least a modest slowing later this year.

The Fed at its September meeting held the target federal funds rate in the current range of from 5.25% to 5.5%, and next meets on Oct. 31 to Nov. 1.

"We think the Fed would like to see a bit more evidence of cooling labor market conditions than we expect," Oxford Economics lead U.S. economist Nancy Vanden Houten wrote this week. The 180,000 jobs she expects the economy added in September would be a slight drop from the 187,000 added in August, and very close to the monthly average seen in the 10 years before the pandemic, from 2010 to 2019.

But she said that wage gains were likely to prove a bit stronger than the month before.

"Data since the August jobs report are consistent with a labor market that is still relatively strong," she said, enough so that the "the risk is still for an additional hike" even if the broad market expectation is that the Fed will not raise rates any further.

The steady job growth and persistent low unemployment rate this year has surprised many economists and policymakers who expected the fast rate hikes of the last year and a half would have done more to slow demand, economic growth and hiring.

This summer brought the first solid evidence of labor market cooling, with three-month average job gains dipping since the start of the year from more than 330,000 as of January to 150,000 for the three months from June through August.

Wage gains have also slowed.

Fed officials delving into the details have found further confidence that a labor market characterized by stunted participation and massive quitting earlier in the pandemic had begun to look more normal - with quit rates, for example, returning to near pre-pandemic levels and the number of jobs for each unemployed person falling sharply.

Data since the Fed met in September also showed underlying inflation slowing even faster than policymakers anticipated when they issued economic projections that continued to see another quarter point rate hike needed by the end of the year.

(Reporting by Howard Schneider; Editing by Andrea Ricci)