U.S. consumer prices recorded their biggest drop in eight months in September as the cost of gasoline fell, but a steady pick-up in the prices of other goods and services suggested inflation was starting to firm.

There was good news on the labor market, with other data on Thursday showing new applications for unemployment aid fell back to a 42-year low last week. The very low level of layoffs and firming underlying inflation could keep the door open to an interest rate increase from the Federal Reserve this year.

The Labor Department said its Consumer Price Index fell 0.2 percent last month after slipping 0.1 percent in August. In the 12 months through September, the CPI was unchanged for the first time in four months after rising 0.2 percent in August.

The so-called core CPI, which strips out food and energy costs, rose 0.2 percent after ticking up 0.1 percent in August. In the 12 months through September, the core CPI increased 1.9 percent, the largest gain since July 2014, after rising 1.8 percent in August.

The Fed tracks the personal consumption expenditures price index, excluding food and energy, which is running well below the core CPI. Low inflation, which has persistently run below the Federal Reserve's 2 percent target, is a major hurdle to an interest rate hike this year.

Prices for U.S. Treasury debt fell on the data, while the dollar rose against the euro.

Fed officials who are divided on when to tighten monetary policy could take comfort in last month's increase in core inflation.

Expectations of a lift-off in the U.S. central bank's short-term interest rate have been dealt a blow by an abrupt slowdown in job growth in the last two months and softening economic activity because of a strong dollar, lower oil prices and a weakening global economy.

"Although the case for a December hike took a hit ... this more-interesting-than-usual core CPI figure will give the hawks something to talk about," said Jennifer Lee, an economist at BMO Capital Markets in Toronto.

In a second report, the Labor Department said initial claims for state unemployment benefits fell 7,000 to a seasonally adjusted 255,000 for the week ended Oct. 10. Claims were last at this level in July, which was the lowest since November 1973.

The low level of layoffs is in sharp contrast with the recent cool-off in employment growth. Nonfarm payrolls growth in August and September averaged 139,000, the weakest two-month rise since January last year.

The slowdown is puzzling given job openings are at record highs. Some economists say the step-down in hiring is because employers cannot find qualified workers for the open jobs.

"Claims continue to show no sign of an uptrend, reinforcing our view that the sudden slowing in payrolls in the last two months mainly reflects volatility rather than a fundamental change in the trend," said Jim O'Sullivan, chief U.S. economist at High Frequency Economics in Valhalla, New York.

The four-week moving average of claims, considered a better measure of labor market trends as it irons out week-to-week volatility, fell 2,250 to 265,000 last week, the lowest level since December 1973.

The inflation report showed gasoline prices fell 9.0 percent, the biggest drop since January, after declining 4.1 percent in August. Food prices increased 0.4 percent, the largest increase since May 2014, after rising 0.2 percent the prior month.

The rental index increased 0.4 percent, after rising 0.3 percent in August. There were increases in the cost of medical care, household furnishings and personal care products. However, apparel prices fell as did the cost of new vehicles and used cars and trucks. Airline fares also declined. 

By Lucia Mutikani - Reuters; (Editing by Andrea Ricci)