In a note, strategists including Aditya Bhave suggested that oil prices, which have remained elevated since the outbreak of the Iran war in late February, are now in a hawkish range for the U.S. central bank.

On Wednesday, U.S. West Texas Intermediate crude futures fell 4.1% to $88.57 per barrel by 5:04 PM Moscow time, while May Brent crude futures—the global benchmark—fell 4.1% to $100.23 per barrel. A Fed rate hike is "most likely" if WTI averages between $80 and $100 per barrel this year. Before the conflict in Iran, WTI was trading around $65 per barrel.

Rising energy prices—caused in large part by the effective closure of the Strait of Hormuz, a crucial waterway south of Iran through which approximately one-fifth of the world's oil passes—have fueled concerns about rising inflationary pressures in countries around the world. In the US, gasoline prices at the pump have already begun to rise and could contribute to overall price increases in the coming months.

A recent S&P Global business activity survey also found that more US companies are beginning to see a spike in commodity costs.

"There is a range of outcomes—when the [oil] shock is persistent but moderate—in which the Fed will become more hawkish because it is more concerned about inflation," BofA analysts said. "Higher rates are far from our baseline scenario, but it's a risk worth considering."

However, analysts argue that there is a "range" of potential outcomes for the Fed.

They added that if the oil shock is temporary and large enough, the initial surge in inflation could soon subside as consumers cut back on spending, putting pressure on demand.

They added that the negative wealth effect from a sustained stock market selloff would then exacerbate the risks of lower employment—the second pillar of the Fed's mandate. Under such circumstances, the central bank would adopt a more accommodative stance, the analysts said.