Israel accuses Hamas Islamists of kidnapping the seminary students, who disappeared last week while hitchhiking from a Jewish settlement.
There has been no word from them since, nor any public claim of responsibility or ransom demands -including by Hamas, though neither has it denied involvement.
A military spokesman said more than 65 Palestinians had been detained overnight, including 51 who were part of a group of 1,027 prisoners released by Israel three years ago in return for soldier Gilad Shalit, who was seized by Hamas in 2006.
Lieutenant-Colonel Peter Lerner said: "We have two efforts ongoing in parallel. First is to bring back the boys, and the second is to take a toll on Hamas for its actions."
Palestinians said the majority of those re-arrested were affiliated with Hamas.