Data published on police website on Thursday indicated that the number of the detentions was above the 3,313 arrivals made last Thursday.
The new arrivals brought the numbers of refugees and migrants looking to move on towards Western Europe from Serbia through Hungary to nearly 22,000 this month alone.
Meanwhile, neighboring Austria has also faced a new rise in numbers of refugees coming from Hungary, as over 3,000 people set foot on its soil overnight.
According to police, between midnight (2200 GMT) and 3:00 a.m. alone, more than 1,700 asylum seekers crossed the border at Nickelsdorf in eastern Austria, while on Thursday morning some 2,800 people were present at the site waiting for special buses and trains to take them to Vienna and beyond.