An interior ministry spokesman rejected calls for a procedural overhaul at the Office for the Protection of the Constitution (BfV), Germany's internal security watchdog.
"We currently have no indication that there are fundamental structural problems," he told reporters, noting that the BfV itself had helped expose the suspect.
"Based on the facts we have, it is too soon to make specific recommendations for action that might arise from this case," which he called isolated.
The agency said on Tuesday that the unnamed 51-year-old German national, who converted to Islam in 2014, had "made Islamist remarks online under a false name, and had offered internal information during online chats".
His chat partner was believed to be another BfV employee.
There was no immediate suggestion that the man, who has been in custody since November 17th, had any ties to terror group Isis.
Prosecutors are readying a case of "preparing a serious act threatening state security". They said the suspect had already made a partial confession.
Before official confirmation of the man's arrest, German media had reported that he was believed to have been planning a bombing at the BfV headquarters in the western city of Cologne.
Der Spiegel and Die Welt said the suspect had partially admitted to the allegations by making references to bomb attacks carried out "in the name of Allah".
But a BfV spokeswoman told AFP that she could not confirm media reports that he was plotting an attack, saying there was no "evidence of a real danger to the office or its workers".
Married with children, he was employed at a bank and had, since April, also been doing some work for the agency gathering intelligence on the Islamist scene in Germany.
Germany has so far been spared the kind of large-scale deadly jihadist atrocities which have been carried out in Paris and Brussels, though individuals have carried out attacks and others have been prevented.