WASHINGTON (Reuters) - U.S. producer prices increased by the most since 2009 in January as the cost of goods and services surged, suggesting inflation at the factory gate was starting to creep up.

The producer price index for final demand jumped 1.3% last month, the biggest gain since December 2009 when the government revamped the series, the Labor Department said on Wednesday. That followed a 0.3% rise in December. In the 12 months through January, the PPI accelerated 1.7% after rising 0.8% in December.

A 1.3% rise in the prices of services accounted for two-thirds of the increase in the PPI. That was the biggest gain since December 2009 and followed a 0.1% drop in December.

The cost of goods surged 1.4% after gaining 1.0% in December. Economists polled by Reuters had forecast the PPI would rise 0.4% in January and gain 0.9% on a year-on-year basis.

Inflation is under focus this year amid concerns from some quarters that President Joe Biden's $1.9 trillion recovery plan could lead to the overheating of the economy. The package, which would follow on the heels of nearly $900 billion in additional COVID-19 pandemic relief from the government in late December, is working its way thorough the U.S. Congress.

Higher inflation is anticipated by the spring as price declines early in the coronavirus crisis wash out of the calculations, but there is no consensus among economists on whether it would stick beyond the so-called base effects.

Federal Reserve Chair Jerome Powell said last week he expected the rise in price pressures would be transitory, citing three decades of lower and stable inflation.

Slack in the labor market remains excessive, with at least 20 million Americans on unemployment benefits.

The government last week reported a moderate rise in consumer prices in January.

Excluding the volatile food, energy and trade services components, producer prices accelerated 1.2% in January. The so-called core PPI increased 0.4% in December. In the 12 months through January, the core PPI rose jumped 2.0% after gaining 1.1% in December.

The Fed tracks the core personal consumption expenditures (PCE) price index for its 2% inflation target, a flexible average. The U.S. central bank has signaled it would tolerate higher prices after inflation persistently undershot its target. The core PCE price index is at 1.5%.

Wholesale energy prices surged 5.1% after rising 4.9% in December. Food prices gained 0.2%. Core goods prices increased 0.8%. A 1.4% jump in prices for final demand services less trade, transportation, and warehousing accounted for more than 70% of the increase in services last month.

Healthcare costs accelerated 1.2%, while portfolio fees soared 9.4%. Those healthcare and portfolio management costs feed into the core PCE price index.

(Reporting by Lucia Mutikani; Editing by Paul Simao)