STRESA, ITALY (Reuters) - An increase in a key euro zone wage indicator is not particularly worrisome and the European Central Bank should be in position to cut interest rates on June 6, Bundesbank President Joachim Nagel said on Friday.

The ECB has long flagged a rate cut next month but a pick up in negotiated wage growth across the 20 nation currency bloc, a long awaited indicator of price pressures has clouded the outlook.

Nagel played down the wage figure, which showed a pick up to 4.7% from 4.5%, arguing that this was a backward looking indicator and he expected benign trends ahead.

"If things stay as they are the probability increases that we could take the first rates step in June," Nagel said at a press conference on the sidelines of a G7 finance ministers' conference in Stresa, Italy.

Nagel said he expected wage trends to "flatten," a possible relief for inflation.

But he also repeated his earlier message that the June rate cut did not carry any sort of commitment about subsequent moves as ECB decisions will be based on incoming data, without any automaticity, a change to policy in recent past when the ECB often flagged expected moves.

Still, some conservatives, including board member Isabel Schnabel, have already argued against back-to-back rate cuts, warning that current inflation and wage trends do not justify further policy easing in July.

Markets have also given up on a quick follow-up cut and they now see just one more rate reduction after June, a big swing compared to the start of this year when up to six moves were predicted.

While most market economists still bet on cuts in June, September and December, Danske Bank on Friday changed its own call, predicting only two rate cuts in 2024.

(Reporting by Christian Kraemer, Writing by Andrey Sychev and Balazs Koranyi; Editing by Rachel More and Toby Chopra)