* Weekly jobless claims hit seven-year low
* Consumer prices post largest gain in 10 months
* Underlying inflation pressures show signs of picking up
WASHINGTON, May 15 (Reuters) - New applications for U.S. unemployment benefits hit a seven-year low last week while consumer prices recorded their largest increase in 10 months in April, pointing to a firming economy.
The economy's outlook was further brightened by other data on Thursday showing factory activity in New York state expanding at its quickest pace in nearly four years in May.
"It conveys the message of solid economic activity. Labor conditions continue to improve and I expect this will be validated by payroll reports over the next few months," said Anthony Karydakis, chief economic strategist at Miller Tabak in New York.
Initial claims for state unemployment benefits declined 24,000 to a seasonally adjusted 297,000, the Labor Department said, offering fresh evidence the jobs market was strengthening.
That was the lowest reading since May 2007 and brought claims back to their pre-recession level. Economists had forecast first-time applications ticking up to 320,000 last week.
In a second report, the department said its Consumer Price Index increased 0.3 percent last month as food prices rose for a fourth consecutive month and the cost of gasoline surged.
The rise in the CPI was the biggest rise since June last year and added to March's 0.2 percent rise.
The combination of a strengthening jobs market and an uptick in inflation pressures should give the Federal Reserve ammunition to continue scaling back its monetary stimulus.
However, the U.S. central bank is not expected to start raising overnight interest rates, currently near zero, before the second half of 2015.
The dollar rose against the euro and the yen on the reports, while prices for U.S. government debt fell. U.S. stock index futures trimmed losses.
In the 12 months through April, consumer prices rose 2.0 percent after gaining 1.5 percent in March. The increase was the biggest since July last year and in part reflected prices coming off last year's low base when energy costs decreased.
Economists had forecast the CPI increasing 0.3 percent from March and gaining 2.0 percent from a year ago.
Stripping out food and energy prices, the so-called core CPI rose 0.2 percent after advancing by the same margin in March.
In the 12 months through April, the core CPI increased 1.8 percent. That was the biggest gain since August last year and followed a 1.7 percent rise in March.
Economists had forecast the core CPI rising only 0.1 percent from March and 1.7 percent from a year-ago.
The Fed targets 2 percent inflation and it tracks an index that is running even lower than the CPI. Policymakers worry that inflation is running too low, but the steady increase in prices should ease those concerns.
Claims had been volatile in recent weeks because of difficulties adjusting the data during the Easter and Passover holidays and school spring breaks, which fall on different calendar days every year.
The four-week moving average for new claims, considered a better measure of underlying labor market conditions as it irons out week-to-week volatility, fell 2,000 to 323,250.
The labor market is strengthening after wobbling in December and January because of an icy-cold winter. Nonfarm payrolls increased 288,000 in April and economists expect job gains to average 200,000 for the rest of the year.
That should stimulate demand and boost economic growth.
The claims report showed the number of people still receiving benefits after an initial week of fell 9,000 to 2.67 million in the week ended May 3, the lowest since December 2007.
Separately, the New York Federal Reserve said its "Empire State" general business conditions index jumped to 19.01 this month, the strongest reading since June 2010. It was at 1.29 in April.
Readings above zero indicate growth. New orders surged after contracting in April and inventories also increased, as did shipments.
(Reporting by Lucia Mutikani, additional reporting by Richard Leong in New York; Editing by Andrea Ricci)