U.S. consumer prices rose modestly last month while a cold snap lifted industrial output, suggesting the economy was growing but not generating enough inflation to trouble the Federal Reserve.

While Friday's data showed the economic recovery remains on track, high unemployment and worries over income continue to weigh on consumer morale.

The Labor Department said its Consumer Price Index rose 0.1 percent last month from November as food and energy costs gained only modestly and housing-related expenses held steady. The index rose 0.4 percent in November.

Analysts polled by Reuters had forecast consumer prices rising 0.2 percent in December.

In a separate report, the Fed said industrial production rose 0.6 percent in December as electric and gas utilities stepped up output in an unusually cold month.

That matched the consensus forecast from economists polled by Reuters. The December gain also matched November's increase, which was initially reported as a 0.8 percent advance.

The Fed said, however, that manufacturing production slipped 0.1 percent, disappointing expectations for a gain.

We think manufacturing activity will be well supported during the positive phase of the inventory cycle. However, it will ultimately need to be propelled by final demand growth, said Julia Coronado, an economist at BNP Paribas in New York.

A reading on consumer confidence from The Reuters/University of Michigan Surveys of Consumers indicated American consumers are still cautious about spending. The survey's preliminary index of sentiment for January was 72.8, up from 72.5 late December and 61.2 a year ago.

The reading was the highest since September 2009, but it fell short of analysts' median expectation of a reading of 73.9, according to a recent Reuters poll.

Another set of data from the New York Federal Reserve Bank showed factory activity in New York State gained steam this month as new orders and shipments surged, suggesting a manufacturing recovery remains in place.

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Long-dated U.S. Treasury debt prices rallied on the inflation data, while the U.S. dollar was steady.

CPI does not appear to be flashing significant inflationary pressure ... and the Fed has nothing to worry about for now, said Michael Woolfolk, senior currency strategist at Bank of New York Mellon in New York.

The Fed has kept benchmark overnight interest rates near zero for more than a year and vowed at its last meeting to hold them low for an extended period. Officials next gather on January 26-27 to plot the course for monetary policy.

Price rises in December slowed as gasoline costs increased 0.2 percent after surging 6.4 percent in November. Food costs increased 0.2 percent last month after gaining 0.1 percent in November.

Compared with December 2008, prices rose 2.7 percent, the largest gain since 2007, the department said.

Excess slack in both the industrial sector and the labor market are keeping inflation pressures muted. The Federal Reserve has promised to keep overnight lending rates near zero for an extended period of time to help the economy recover from its worst recession in 70 years.

Stripping out volatile energy and food prices, the closely watched core measure of consumer inflation edged up 0.1 percent in December after being flat the prior month. That was in line with market expectations for a 0.1 percent gain.

Core prices were lifted by rising prices for used cars and trucks, but shelter costs were flat and prices for new vehicles fell. High vacancy rates are keeping rentals depressed.

Compared with December 2008, the core inflation rate rose 1.8 percent, after increasing 1.7 percent in November.

(Reporting by Lucia Mutikani and Emily Kaiser in Washington; Editing by Andrea Ricci and Dan Grebler)