* Producer price index falls 0.3% in September
* PPI increases 1.4% year-on-year
* Core PPI unchanged; rises 1.7% year-on-year
WASHINGTON, Oct 8 (Reuters) - U.S. producer prices unexpectedly fell in September, leading to the smallest annual increase in nearly three years, which could give the Federal Reserve room to cut interest rates again later this month.
The weak producer inflation readings reported by the Labor Department on Tuesday came against the backdrop of a slowing economy amid trade tensions and cooling growth overseas. The Fed cut rates in September after reducing borrowing costs in July for the first time since 2008, to keep the longest economic expansion on record, now in its 11th year, on track.
The producer price index for final demand dropped 0.3% last month, weighed down by decreases in the costs of goods and services, the government said. That was the largest decline since January and followed a 0.1% gain in August.
In the 12 months through September the PPI increased 1.4%, the smallest gain since November 2016, after rising 1.8% in August. Economists polled by Reuters had forecast the PPI nudging up 0.1% in September and advancing 1.8% on a year-on-year basis.
Excluding the volatile food, energy and trade services components, producer prices were unchanged last month after jumping 0.4% in August. The so-called core PPI increased 1.7% in the 12 months through September after climbing 1.9% in August.
The Fed, which has a 2% annual inflation target, tracks the core personal consumption expenditures (PCE) price index for monetary policy. The core PCE price index rose 1.8% on a year-on-year basis in August and has undershot its target this year.
Some economists expect the U.S. central bank could cut rates at its Oct. 29-30 policy meeting amid signs that the Trump administration's 15-month trade war with China, which has weighed on business investment and pushed manufacturing into recession, was impacting the broader economy.
While the unemployment rate dropped to near a 50-year low of 3.5% in September, hiring slowed significantly, with the three-month average gain in private payrolls falling to 119,000 jobs, the smallest since July 2012, from 135,000 in August.
In addition, private services industry growth slowed to a three-year low in September.
U.S. financial markets were little moved by the producer inflation data.
In September, wholesale energy prices fell 2.5%, matching August's decline. They were pulled down by a 7.2% decline in gasoline prices, which followed a 6.6% percent drop in August.
Gasoline accounted for three quarters of the 0.4% drop in goods prices last month. Goods prices decreased 0.5% in August. In the 12 months through September, goods prices dropped 0.5%, the most since August 2016.
Wholesale food prices rebounded 0.3% in September, lifted by a 26.8% surge in the cost of chicken eggs. Food prices dropped 0.6% in August. Core goods prices fell 0.1% last month. They were unchanged in August.
The cost of services fell 0.2%, the most since February 2017, after increasing 0.3% in August. Services were dragged down by a 1.0% drop in trade services, which measure changes in margins received by wholesalers and retailers.
Nearly half of the drop in services was attributed to a 2.7% decrease in machinery and vehicle wholesaling.
The cost of healthcare services rose 0.3% after rising 0.2% in August. The cost of hospital outpatient care surged 1.1%, the biggest rise since 2014, after slipping 0.1% in August. There were gains in the costs of doctor visits and hospital inpatient care.
Portfolio management fees were unchanged last month after increasing 0.5% in August. Those fees and healthcare costs feed into the core PCE price index. (Reporting by Lucia Mutikani; Editing by Andrea Ricci)