Swastikas were scratched into the door of the prayer hall of the Jewish section of Liverpool's Springwood cemetery at the weekend - and another was daubed on a south Liverpool bus stop.
The bus stop swastika was quickly removed and Merseyside Jewish Representative Council chair Ian Cohen said on Tuesday that Liverpool City Council, which administers the cemetery, had prioritised the removal of the graffiti. It had been the first such incident for a number of years.
There had been "excellent co-operation from the city council and the police" and the desecration was being treated as a hate crime.
Police have issued an appeal for witnesses.