Euro zone inflation remains too high, so further European Central Bank policy tightening is necessary, even if there is a growing body of evidence that past rate hikes are staring to work, ECB President Christine Lagarde said on Thursday.

The ECB has lifted rates by a combined 375 basis points since July and essentially promised another move in June, despite fresh data showing inflation easing far more than expected in May to 6.1%.

"Today, inflation is too high and it is set to remain so for too long," Lagarde said in a speech.

"That is why we have hiked rates at our fastest pace ever – and we have made clear that we still have ground to cover to bring interest rates to sufficiently restrictive levels," she added.

These hikes are already raising bank rates "forcefully" and there is still plenty of tightening in the pipeline but the ECB is uncertain just how much stronger the transmission of its policy will be, Lagarde said.

"So, we need to continue our hiking cycle until we are sufficiently confident that inflation is on track to return to our target in a timely manner," she said, referring to the bank's medium-term inflation target of 2%.

While many policymakers have already put a July rate hike on the table even before the June 15 meeting takes place, some economists said that benign inflation data out on Thursday could mean the end of hikes already this month.

This is still not the main scenario, however, according to investors, who still price two more rate hikes, and policymakers rarely change their views on a single piece of data.

Part of the problem is that underlying price growth is stubbornly high.

"There is no clear evidence that underlying inflation has peaked," Lagarde said. "Labour markets across the euro area are tight and workers have considerable bargaining power, which they are starting to use to recoup these losses." (Reporting by Balazs Koranyi; Editing by Jon Boyle and Susan Fenton)