The Federal Aviation Office (LBA) told the Welt am Sonntag newspaper that parent company Lufthansa had given it "no information about the medical background" of Lubitz, who prosecutors allege deliberately crashed the plane, killing all 150 people on board.
In particular, Lufthansa physicians who examined Lubitz did not make the authorities aware of his "earlier phase of serious depression", the report quoted the LBA, which issues pilots' licences, as saying.
Welt am Sonntag said that Lubitz had been tested at least six times by Lufthansa doctors since 2009 but after a psychological test was ordered that year, no further mental health evaluations were carried out.
The newspaper quoted Lufthansa as saying that it declined to comment due to the ongoing investigation into the crash of the flight bound for the western German city of Duesseldorf from Barcelona.
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The LBA could not immediately be reached for comment.
But the German flag carrier acknowledged last week that Lubitz had informed its flight school in mid-2009, when resuming training after a lengthy medical absence, that he had suffered from "previous episode of severe depression".
He later received the medical certificate confirming he was fit to fly.
German prosecutors said last week that Lubitz was diagnosed as suicidal "several years ago", before he became a pilot, but doctors had recently found no sign he intended to hurt himself or others.
Ripped up sick notes were found in a flat used by Lubitz, which authorities believe indicates that the 27-year-old was trying to hide his illness from his employer.
A European Aviation Safety Agency spokeswoman told AFP yesterday that it had voiced concerns over Germany's "non-conformity" with air safety rules before the crash, especially on air crew health monitoring.