ROME (Reuters) - The European Central Bank can continue to gradually reduce interest rates without jeopardising the current fall in inflation, governing council member Fabio Panetta said on Tuesday.

The ECB cut rates for the first time in June from their record highs but has made no explicit commitment about a follow up move.

"The reduction of official rates can proceed gradually, accompanying the return of inflation towards the objective, if macroeconomic trends remain in line with the ECB's expectations," Panetta said in a speech to bankers in Rome.

Panetta, the governor of the Bank of Italy, is widely considered a monetary policy dove.

He played down concerns over persistently high service sector prices, saying it was normal that they should fall with a lag compared to goods prices, and he said wage growth can also be expected to moderate.

"Past interest rate hikes are still dampening demand, output and inflation and will continue to do so in the months to come," Panetta said.

(Reporting By Gavin Jones, editing Gianluca Semeraro)