"The erroneous account numbers have been corrected for the vast majority of unemployment benefit recipients. Thanks to the support of credit institutions, almost all those eligible will have the payment by January 3 at the latest," the Labour Office said in a statement.
It did not, however, say how many welfare recipients might still not get their money on time and no one was available for comment at the office itself.
Those without money by Monday could get an advance payment from their local labour offices, the statement said.
The delay coincides with the introduction of the so-called "Hartz IV" labour market reforms, which are expected to cut payouts for around one million unemployed Germans and will make it more difficult to qualify for benefit.
Complex new software had to be installed across Germany for the new benefit system. German firm T-Systems, which helped in the transformation, said the problem was with the Labour Office's software, rather than its own.
The measures sparked a public outcry earlier this year, bringing tens of thousands of Germans into the streets, mainly in the depressed eastern part of the country.
Those demonstrations faded since their peak in August. But organisers are threatening to come out in force on Monday to protest the start of the reforms, which have been hailed as the biggest change to Germany's welfare system since World War Two.