FRANKFURT (Reuters) -The European Central Bank needs to keep raising interest rates, policymakers said on Friday, reaffirming the bank's stance after fresh projections showed that inflation is even more stubborn than feared.

The ECB raised interest rates to 22-year high of 3.50% on Thursday and said it would move again in July, continuing what has been the fastest pace of monetary tightening in the bank's quarter century existence.

Among the most hawkish comments, Bundesbank President Joachim Nagel said the July move, essentially promised by ECB President Christine Lagarde, could easily be followed by other steps.

"We still have more ground to cover," he said in a speech after the ECB flagged a July rate hike but made no commitment for subsequent moves. "We may need to keep raising rates after the summer break."

He added: "Once we have reached the peak, we will stay there until we are sure of a safe and timely return of inflation to our 2% target."

Lithuania's central bank chief, Gediminas Simkus, took a more nuanced view, arguing that more policy tightening is needed but the ECB was nearing the peak and it was too early to make a commitment about where rates would be in the autumn.

"Inflation has been too high for too long," Simkus told reporters. "Over the medium term, inflation is not coming back to an appropriate level."

Simkus also pushed back on market expectations for early 2024 rate cuts, arguing that such a rapid reversal would be puzzling.

Joining the chorus, Estonian central bank chief Madis Muller said more rate action is needed.

"Euro zone interest rates have not yet peaked," Muller said in a statement. "The ultimate goal is clear for the central bank: we need to quickly get the price rise under control."

Finland's central bank chief Olli Rehn, considered a centrist swing voter, repeated the ECB's stance that rates are not yet at their peak but said future moves depended on the outlook.

"The key ECB interest rates will be brought to levels sufficiently restrictive to achieve a timely return of inflation to the 2% medium-term target and will be kept at those levels for as long as necessary," Rehn said.

(Reporting by Balazs Koranyi, Andrius Sytas and Terje Solsvik; Editing by Alex Richardson and Toby Chopra)