* Jobless claims fall 3,000 in February payrolls survey week
* Consumer prices up a bit in January, heating costs jump
By Lucia Mutikani
WASHINGTON, Feb 20(Reuters) - The number of Americans filing new claims for unemployment benefits fell last week, pointing to steadily improving labor market conditions, despite two straight months of weak hiring.
Other data on Thursday showed relentlessly cold weather putting a strain on household budgets, with electricity and heating fuel prices surging in January. However, inflation pressures remained muted.
Initial claims for state unemployment benefits declined 3,000 to a seasonally adjusted 336,000, the Labor Department said. That was mostly in line with economists' expectations.
The claims data covered the survey week for February's nonfarm payrolls report. Snow storms slammed parts of the country last week, which could have kept some workers at home.
Bitterly cold weather was blamed for a sharp slowdown in hiring in December and January's marginal bounce back. Claims have been tucked in a 325,000-348,000 range this year suggesting no fundamental shift in labor market conditions.
In a second report, the department said strong gains in the price of household energy had accounted for most of the 0.1 percent rise in its Consumer Price Index in January.
The CPI had advanced 0.2 percent in December and last month's rise was in line with economists' expectations.
In January, electricity prices rose 1.8 percent, the largest gain since March 2010. Natural gas prices surged 3.6 percent. That was the largest rise since April. The cost of heating oil jumped 3.7 percent, the biggest increase since September 2012.
The increases, which offset a 1.0 percent fall in the price of gasoline, a putting a strain household finances as incomes barely grow.
In a third report, the department said weekly average earnings adjusted for inflation rose 0.1 percent in January after sliding 0.5 percent in December.
U.S. financial markets were little moved by the data.
Consumer prices advanced 1.6 percent in the 12 months to January, after increasing 1.5 percent in December.
Stripping out the volatile energy and food components, the so-called core CPI also rose 0.1 percent in January for a second straight month. In the 12 months to January, core CPI rose 1.6 percent, slowing from a 1.7 percent increase in December and the smallest rise since June.
With consumer inflation continuing to run below the Federal Reserve's 2 percent target, monetary policy is likely to remain accommodative for a while even as the U.S. central bank reduces the amount of money it is injecting into the economy each month.
Within the core CPI, there were increases in rents, medical care costs and prescription drugs. Tobacco prices recorded their largest gain since July. These tend to rise at the beginning of the year because of tax hikes.
Elsewhere, there were declines in the price of new motor vehicles, prices for used cars and trucks and apparel. Airline fares dropped 2.2 percent.