The ECB has raised rates by 350 basis points since July, including three back-to-back 50 basis point increases, but has not given any steer about its May 4 meeting, arguing that incoming data will guide its decision.
Markets price in another 75 bps of hikes during the bank's current tightening cycle.
"The persistence of inflation currently argues for another 50 basis points (in May)," Holzmann told Boersen Zeitung in an interview. "If we do not act vigorously enough now, the inflation problem will only increase and we will end up being even stricter."
ECB chief economist Philip Lane has argued that if the economy develops along the path seen in the bank's March projections, more rate hikes will be needed to get inflation back down to 2%.
Few policymakers have put a number on the May 4 decision after volatility in the bank sector last month changed the outlook in a matter of days.
Holzmann has often represented the most hawkish view on the 26-member Governing Council and has been at times alone in some of his views.
"There is a great deal of common understanding in the ECB Governing Council that we have not yet reached the end of the line when it comes to key interest rates," Holzmann said. "We must continue to act decisively and continue to raise key interest rates noticeably even beyond May."
(Reporting by Balazs Koranyi; editing by John Stonestreet)
