Rhineland-Palatinate minister-president Malu Dreyer said on the weekend that the Federal Office for Migration and Refugees (BAMF) was working too slowly and shouldn't be taking weekends off during the crisis.
On Monday, the Passauer Neue Presse (PNP) reported that 964,574 refugees had arrived in Germany by the end of November, based on figures the Interior Ministry gave in response to a parliamentary question.
That's more than four times as many as arrived in 2014, when the total for the whole year was 238,676.
The BAMF still faces a backlog of 355,914 cases, the PNP reported.
But Chancellor Angela Merkel's chief of staff Peter Altmaier – who has overall responsibility for refugees - leapt to the defence of BAMF boss Frank-Jürgen Weise on Sunday.
Altmaier told broadcaster ARD on Sunday evening that Weise "has only been in office for a few weeks, and an unbelievable amount has been done in this time".
Altmaier said that in spite of massively increased numbers of asylum applications, the BAMF had managed to cut down the time it takes to make decisions.
"That's why I don't think it's productive when whoever it is thinks they can make political declarations off the backs of the workers" at the BAMF, he said.
Labour Minister Andrea Nahles told broadcaster ZDF that things would really pick up at the BAMF after the new year, when 4,000 new officials would join the office.
"Then there will be a big step forward," she said.