WASHINGTON, April 9 (Reuters) - New applications for U.S. unemployment benefits increased moderately last week, showing no signs of labor market deterioration, potentially giving the Federal Reserve room to keep interest rates unchanged as it monitors the economic fallout from the war with Iran.

Initial claims for state unemployment benefits rose 16,000 to a seasonally adjusted 219,000 for the week ended April 4, the Labor Department said on Thursday. Economists polled by Reuters had forecast 210,000 claims for the latest week. Low layoffs are anchoring the labor market, and so far there is no indication that employers have responded to the oil price shock from the U.S.-Israel war with Iran by reducing headcount.

President Donald Trump on Tuesday announced a two-week ceasefire on condition of Tehran reopening the blockaded Strait of Hormuz. A surge in global oil prices has sent the national average gasoline retail price soaring above $4 per gallon for the first time in more than three years and wiped off about $3.2 trillion from the stock market in March.

Economists are bracing for a jump in inflation in March, with the Consumer Price Index expected to increase by as much as 1.0% on a monthly basis, translating to a year-on-year rise of about 3.3%. The U.S. central bank has a 2% target.

Minutes of the Fed's March 17-18 policy meeting released on Wednesday showed a growing group of policymakers felt last month that rate hikes might be needed to counter inflation.

The Fed left its benchmark overnight interest rate in the range of 3.50%-3.75%. The odds of a rate cut this year have greatly diminished. The majority of policymakers "expected the unemployment rate to remain little changed and for net job creation and labor force growth to remain low, while a couple of participants (in the policy meeting) expected labor market conditions to soften," the minutes showed. 

The labor market has been stuck in what economists call a "low-hire, low-fire" state which they blamed on uncertainty stemming from Trump's import tariffs and mass deportations.

Though nonfarm payrolls rebounded by 178,000 jobs in March, the median duration of unemployment at 11.4 weeks was the longest in nearly 4-1/2 years. 

The number of people receiving unemployment benefits after an initial week of aid, a proxy for hiring, decreased 38,000 to a seasonally adjusted 1.794 million during the week ended March 28, the claims report showed.

While the so-called continuing claims have dropped from last year's lofty levels, that's likely because of people exhausting their eligibility for benefits, limited to 26 weeks in most states. Some unemployed young adults, who typically have a limited or no work history, are not eligible to file for jobless benefits. They have been the worst affected by the lethargic labor market.