“The house is on fire,” DBB boss Klaus Dauderstädt told the Westdeutsche Allgemeine Zeitung (WAZ) on Monday.
“We need a push for personnel to get young people enthusiastic about the public sector.”
The report, seen by WAZ, found that the worst personnel holes were in local government.
120,000 teachers, especially scientists, and 10,000 more policemen were needed to match the quantity of work, the unions said..
And they called for thousands of new firemen, Jobcenter staff, doctors and food chemists.
They said that in recent years there have been explicit efforts to reduce staff numbers, while public servants are seen as having “an unattractive pay package”.
“If a private employer sees that he's not finding the engineer, doctor or IT specialist he's after, he adds another thousand to the salary. Communes, social security and the tax office can't do that,” Dauderstädt said.
He added that up to 80 percent of new hires in the public sector were placed on temporary contracts.
The problem is only set to get worse in the coming years, the DBB says.
“Public servants have an average age of 45 years, that means that in the next 20 years 1.5 million will retire,” a DBB spokeswoman told The Local.
“That will make the lack of personnel much worse.”
She added that many open positions can't be filled due to the more attractive salaries on offer elsewhere.
“We haven't seen the study and we can't say how they've arrived at these numbers,” a spokeswoman for the Federation of Communal Employers (VKA) told The Local.
“As far as we're concerned, the number of people working in communes - 2.1 million - is stable and has been rising in recent years.”
But there have been regular reports of difficulties filling positions in daycare centres (Kita), especially since new legislation came into effect last year making daycare a right for all children over one year old.
A Federal Labour Agency (BA) spokesman contacted by The Local would not comment on the figures.