* Weekly jobless claims fall 3,000
* Produce price index rises 0.1 percent in June
* Core PPI increases 0.2 percent
* PPI gains 2.0 percent year-on-year; core PPI up 2.0 percent
WASHINGTON, July 13 (Reuters) - The number of Americans filing for unemployment benefits fell last week for the first time in a month and producer prices unexpectedly rose in June, likely keeping the Federal Reserve on track for a third interest rate increase this year.
Persistently low layoffs point to a buoyant labor market that is sustaining economic growth, while the uptick in producer prices suggests a recent moderation in inflation was likely temporary.
Initial claims for state unemployment benefits dropped 3,000 to a seasonally adjusted 247,000 for the week ended July 8, the Labor Department said on Thursday
Claims have now been below 300,000, a threshold associated with a healthy labor market, for 123 straight weeks. That is the longest such stretch since 1970, when the labor market was smaller. The labor market is near full employment, with the jobless rate at 4.4 percent.
The drop in first-time applications for jobless benefits came on the heels of data last week showing the economy created 222,000 jobs last month, the second biggest payrolls increase this year.
The number of Americans on unemployment rolls dropped 20,000 to 1.95 million in the week ended July 1. The so-called continuing claims have now been below 2 million for 13 straight weeks, pointing to shrinking labor market slack.
A Fed survey of the economy published on Wednesday showed "labor markets tightened further for both low and high-skilled positions, particularly in the construction and IT sectors."
Prices for U.S. Treasuries fell, with the yield on the 30-year government bond hitting a session high. The dollar was trading slightly lower against a basket of currencies.
PRODUCER PRICES NUDGE UP
In another report, the Labor Department said its producer price index for final demand edged up 0.1 percent last month after being unchanged in May.
In the 12 months through June the PPI increased 2.0 percent, slowing after May's 2.4 percent advance as last year's energy-driven rise drops out of the calculation.
Economists polled by Reuters had forecast the PPI being unchanged last month and rising 1.9 percent from a year ago.
A key gauge of underlying producer price pressures that excludes food, energy and trade services increased 0.2 percent last month. The so-called core PPI fell 0.1 percent in May.
The core PPI increased 2.0 percent in the 12 months through June after climbing 2.1 percent in May.
Fed officials are closely watching inflation, which has remained below the U.S. central bank's 2 percent target for five years. They have largely viewed the recent retreat in price pressures as transitory.
Labor market strength and signs of an uptick in inflation could bolster expectations that the Fed will raise interest rates in December for a third time this year and announce in September a plan to start reducing its $4.2 trillion portfolio of Treasury bonds and mortgage-backed securities.
Fed Chair Janet Yellen told lawmakers on Wednesday that the economy was healthy enough for the central bank to raise rates and begin winding down its massive bond portfolio.
Last month, prices for services gained 0.2 percent, accounting for almost 80 percent of the increase in the PPI.
Services were lifted by a 0.3 percent rise in the index for final demand trade services, excluding transportation and warehousing. It was the fourth straight monthly increase in services and followed a 0.3 percent gain in May.
The cost of healthcare services were unchanged after dipping 0.1 percent in May. Those costs feed into the Fed's preferred inflation measure, the core personal consumption expenditures price index.
Energy prices fell 0.5 percent after declining 3.0 percent in May. Food prices jumped 0.6 percent in June following a 0.2 percent drop the prior month.
(Reporting By Lucia Mutikani; Editing by Andrea Ricci)