WASHINGTON, March 26 (Reuters) - New applications for U.S. unemployment benefits rose slightly last week, suggesting the labor market remains stable and giving the Federal Reserve scope to hold interest rates steady while monitoring inflation risks linked to the Middle East conflict.

Initial claims for state unemployment benefits increased 5,000 to a seasonally adjusted 210,000 for the week ended March 21, the Labor Department said on Thursday. Economists polled by Reuters had forecast 210,000 claims for the latest week.

Claims have been tucked in a 201,000-230,000 range this year amid low layoffs.

Economists said lingering uncertainty caused by President Donald Trump's aggressive import tariffs has undercut demand for workers, with private nonfarm payrolls averaging only 18,000 jobs per month in the three months through February. Reduced labor supply because of the Trump administration's hard-line immigration policy was also weighing on job growth, they said.

That has created what Fed Chair Jerome Powell this month called a "zero employment growth equilibrium," that has "a feel of downside risk." 

Though economists are expecting labor market stability to persist, the U.S.-Israeli war with Iran has sparked worries of a surge in inflation. Oil prices have jumped more than 30% since the conflict started at the end of February. 

Import and producer prices shot up in February, and economists expected the hit from the war, which has also raised fertilizer prices, to be evident in March consumer inflation data. Economists have been steadily raising their inflation forecasts for this year as the conflict drags on. 

The U.S. central bank this month left its benchmark overnight interest rate in the 3.50%-3.75% range. Policymakers projected only a single reduction in borrowing costs this year. Financial markets see the odds of a rate cut fading.

The number of people receiving unemployment benefits after an initial week of aid, a proxy for hiring, decreased 32,000 to a seasonally adjusted 1.819 million during the week ended March 14, the claims report showed. The so-called continuing claims data covered the period during which the government surveyed households for March's unemployment rate.

While continuing claims have declined from last year's lofty levels, that could partly reflect some people exhausting their eligibility for benefits, limited to 26 weeks in most states. 

Last year's unemployed college graduates are not captured in the data as they are not eligible for benefits because they most likely have a limited or no work history. The unemployment rate increased to 4.4% in February from 4.3% in January.