Yiannis Mouzalas told a news conference that Greek and UN services had recorded 54,000 refugees and migrants on Greek territory between June and the end of July.
Over 41,000 of them on the mainland have expressed interest in asylum, or have made formal requests.
Another 2,000 have agreed to be returned home.
At the same time, there are another 11,000 people currently being processed on Greek islands after landing there from neighbouring Turkey.
Mouzalas said the operation was designed to "begin to rein in the chaos", which overwhelmed Greek authorities after a succession of Eastern European and Balkan countries shut their borders to migrants starting in February.
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The migration minister admitted that there are additionally "around 4,000" people who are avoiding follow-up registration as they hope to cross the border with the help of smugglers.
But Mouzalas denied reports that hundreds of people were being allowed to sneak across the border to Macedonia and Bulgaria.
"This is a lie," he said. "If 700 were leaving every day (as is claimed) we'd have no refugees left (in Greece).