FRANKFURT (Reuters) - The European Central Bank should not necessarily follow up a rate cut in June with another move the following month, even if inflation is on its way to target, Bundesbank President Joachim Nagel said in a newspaper interview published on Tuesday.

The ECB has all but promised a rate cut on June 6, so policymakers have shifted their attention to debating where rates will go thereafter.

While some are advocating for further cuts, others including board member Isabel Schnabel, Belgium's Pierre Wunsch, the Netherlands' Klaas Knot and Latvia's Martins Kazaks have suggested that a second cut in July may be premature.

"If rates are lowered for the first time in June, that does not mean we will cut rates further in subsequent Governing Council meetings," Nagel said during a joint interview with Germany's Handelsblatt, France's Les Echos, Italy's Corriere della Sera and Spain's El Mundo. "We are not on auto-pilot."

Nagel said that inflation, last measured at 2.4%, would fluctuate around current levels for a few months before resuming a downward trend towards the ECB's 2% target.

"There may well be months where inflation picks up a little, as some prices tend to fluctuate - energy prices in particular," Nagel said. "On the whole, I expect inflation to carry on declining towards our 2% target and to reach it in 2025."

Nagel was sanguine on wages, the ECB's biggest worry this year, arguing that trends were heading in the right direction and there were no signs of a self-reinforcing wage-price spiral.

(Reporting by Balazs Koranyi; Editing by Bernadette Baum)