May 29 (Reuters) - Federal Reserve Vice Chair for Supervision Michelle Bowman said on Friday the Middle East war's impact on the economy, while still being measured, could lead to persistent rises in inflation that might require tighter monetary policy.

"It still seems early to assess the size and persistence of the economic effects from the Iran conflict," Bowman said in the text of a speech to be delivered at a conference in Iceland.

She said she was "optimistic" that once the war is over, supply disruptions will end and there will be a "temporary" impact on inflation and a "minimal" hit to overall economic activity. But Bowman added, "should disruptions persist well into the second half of the year, we could start to see broader effects on inflation."

She warned, however, that an extended war could change the outlook on monetary policy. If the energy shock that's pushing up inflation were to broaden out into price pressures more broadly, "the more likely I will consider shifting my approach to thinking about the balance of risks," she said.

The Federal Reserve is widely expected to leave its benchmark interest rate in the 3.50%-3.75% range at its June 16-17 policy meeting. Due to the massive spike in energy prices pushing up inflation pressures, central bank officials have backed away from predictions of eventual rate cuts, as some officials have started speculating about the prospect of rate hikes.

Inflation has been well above the Fed's 2% target for years. In the view of many policymakers, the persistent overshoot has made it harder to look through the latest inflation shock as a temporary event. Financial markets expect the central bank's next move will be a hike, although they don't see that shift as imminent.

Bowman, who in recent months has supported easing monetary policy, said in her remarks that she supported keeping language in the Fed's April 29 policy statement that suggested the next move would be a rate cut.

She also said "it is appropriate to look through temporarily elevated inflation readings largely due to higher energy prices, provided that we remain credible in our commitment to achieve our inflation goal and one-off tariff effects wane."

Bowman added that "reacting to temporarily elevated energy price inflation would add unwarranted policy restraint, weighing unnecessarily on economic activity and labor market conditions."

She said the economy has been "resilient" in the face of a labor market vulnerable to shocks.