May 29 (Reuters) - Federal Reserve officials continued on Friday to signal the U.S. central bank may need to raise interest rates in the future if the war in the Middle East leads to a persistent increase in already-high inflation.

The potential shift in the monetary policy outlook has even been embraced by Fed Vice Chair for Supervision Michelle Bowman, one of the central bank's most dovish policymakers. Bowman told a conference in Iceland on Friday that the war and its resulting energy shock could change her view on the outlook for rates.

"It still seems early to assess the size and persistence of the economic effects from the Iran conflict," she said, adding, however, that "should disruptions persist well into the second half of the year, we could start to see broader effects on inflation."

If that happened, Bowman noted that it was more likely that she would "consider shifting my approach to thinking about the balance of risks."

She stopped short of saying such an environment would require rate hikes.

A number of Bowman's colleagues are worried it may be hard to shrug off the current energy shock as a temporary factor, especially because inflation has remained above the Fed's 2% target for many years. That view has led to a willingness by these officials to consider lifting rates to bring price pressures back in line.

Financial markets are betting the Fed's next move will be to raise its benchmark interest rate from the current 3.50%-3.75% range, likely by year's end. Before the start of the U.S.-backed war with Iran, which has led to massive supply chain distortions and an energy price surge, Fed officials had been eyeing a rate cut.

Speaking to a business group in New Jersey, Philadelphia Fed President Anna Paulson said on Friday that monetary policy is "well positioned" considering the unacceptably high inflation pressures and economic uncertainty.

Paulson added that the Fed is ready "to react," and while she sees U.S. monetary policy in the right place, "I think it is healthy that market participants have taken on board scenarios where the (federal) funds rate remains unchanged for an extended period, as well as scenarios where further tightening becomes necessary."

But as San Francisco Fed President Mary Daly put it in an interview with Maria Bartiromo on Fox Business Network, "there's no urgency to make an adjustment" on interest rates.

"Policy is in a good place," she added - a phrase Fed policymakers often use to signal they are comfortable keeping the policy rate where it is - and said any future move may hinge on when the Iran war actually ends.

Oil futures fell more than 2% on Friday and were on track for their steepest weekly decline since early April after reports that the U.S. and Iran had reached agreement to extend their ceasefire for another 60 days.

WORRYING INFLATION DATA

If oil futures prices "start to drift up because the conflict is persistent, well, then that would change my mind on the outlook for the economy in terms of inflation," Daly said.

She'll also be watching whether services industries start to raise prices, a worrying sign that inflation may become more persistent. So far she detects little of that outside of industries where fuel costs are a big chunk of the overall business.

Still, inflation risks are clearly mounting for the Fed, at least in the near term.

A New York Fed gauge designed to capture underlying inflation dynamics jumped to 4% in April from 3.5% in March, according to data released on Friday. Prices of goods and services excluding housing accelerated in April relative to the prior month.

Additionally, data released by the U.S. government on Thursday showed the Personal Consumption Expenditures Price Index rose to 3.8% on a year-over-year basis in April from 3.5% in March.

Kansas City Fed President Jeffrey Schmid, speaking at the same conference as Bowman, said his "primary concern is inflation, which is too hot and has been above target for too long." He added that the textbook strategy of looking through an energy shock as something that won't have a lasting impact is not viable right now.

Schmid also nodded toward the prospect of using the Fed's balance sheet to help pump the brakes on price pressures.

"We're not very restrictive at this stage and I think there's some dialogue that ... we need to start considering what tools we have to really make it a little bit more restrictive," depending on how the ​oil shock plays out.

"Maybe we look at the balance sheet again as another tool to ... create ​some restriction," Schmid said, indicating some sort of new drawdown in Fed holdings could create the needed headwinds for economic growth.

His view on the balance sheet is likely to be at odds with that of Fed Chairman Kevin Warsh, who has expressed skepticism about using the central bank's bond holdings to augment its interest rate policy.

Money market conditions and the Fed's rate-control toolkit also limit how far those holdings can be shrunk without creating market volatility. The central bank is currently rebuilding liquidity after conditions tightened late last year.