A "majority" of Federal Reserve officials believed the central bank could raise interest rates if inflation stays high, according to the minutes from the central bank's April 28-29 policy meeting. Why it matters: It suggests that a larger constituency than previously known is backing the possibility of higher interest rates, with the fallout from the Iran war stoking quicker price increases ahead of Kevin Warsh becoming Fed chair. Between the lines: The Fed held rates steady last month, though much of the disagreement was about language in the closely watched policy statement, which indicated that the next move could be a cut. Four officials on the Fed's rotating roster of voting members dissented, three of whom preferred a more "two-sided characterization" that suggested the Fed's next move could be up or down. What they're saying: "A majority of participants highlighted ...…