WASHINGTON, April 8 (Reuters) - A growing group of Federal Reserve policymakers felt last month that interest rate hikes might be needed to counter inflation that continued to exceed the central bank's 2% target, particularly given the inflationary impact of the U.S.-Israeli war with Iran, according to the minutes of their March 17-18 meeting.

"Some participants judged that there was a strong case for a two-sided description of the (Federal Open Market) Committee's future interest rate decisions in the post-meeting statement, reflecting the possibility that upwards adjustments to the target range for the federal funds rate could be appropriate if inflation were to remain at above-target levels," the minutes said.

At the January meeting a smaller group of "several" officials were willing to open the door to possible rate hikes, but by March and the outbreak of the war "many participants pointed to the risk of inflation remaining elevated for longer than expected amid a persistent increase in oil prices."

The Fed in March held its benchmark overnight interest rate steady in the 3.50%-3.75% range while nodding to the fresh uncertainty the war had introduced to the economic outlook.

Despite the inflation risks, however, "many participants" still saw rate cuts as part of their baseline outlook, with "most participants" judging that an extended conflict in the Middle East would do enough damage to economic growth that even more cuts would be warranted.

"Most participants raised the concern that a protracted conflict in the Middle East could lead to a further softening in labor market conditions, which could warrant additional rate cuts, as substantially higher oil prices could reduce households' purchasing power, tighten financial conditions, and reduce growth abroad," the minutes said.

WAR DISRUPTED OUTLOOK

The minutes were released on Wednesday, a day after the U.S. and Iran agreed to a two-week ceasefire. The news caused oil prices to drop more than 15% to around $92 a barrel.

The back and forth among policymakers at the meeting last month highlighted how the conflict in the Middle East, which disrupted global shipping and caused the price of oil to jump more than 50%, was pulling the Fed in conflicting directions, threatening both its inflation goal and full employment mandate.

At the meeting, the Fed signaled it was unlikely to change its policy rate until it was clearer whether the impact on inflation or the job market seemed to be the greater risk. In new economic projections issued alongside its policy statement, officials penciled in higher inflation for the year, but little change in the unemployment rate.

In presentations at the meeting, Fed staff saw risks that economic and job growth would be weaker and inflation higher than expected in their January outlook, given "the potential economic effects of developments in the Middle East, government policy changes, and the adoption of AI."

Given inflation above target since 2021, "a salient risk was that inflation could prove to be more persistent than the staff anticipated."