"The abduction of 16-year-olds is a terrible crime," he said.
"There are lines that should not be crossed."
Frenkel said the family first realised Naftali had gone missing early on Friday and has slept very little since then.
Israeli Prime Minister Benjamin Netanyahu has said he holds Palestinian president Mahmud Abbas, who recently signed a unity deal with Hamas, responsible for the safety of Frenkel and the two other missing youths: 15-year-old Gilad Shaer and 19-year-old Eyal Ifrach.
The three teenagers were first reported missing late on Thursday but so far there has been no formal claim of responsibility.
Israel has arrested more than 150 Palestinians in one of the biggest sweeps in recent years, with the searches focusing on the southern West Bank city of Hebron and the surrounding area.
The teens' disappearance has captured the hearts of the nation, with some 20,000 Israelis pouring into the Western Wall plaza in the Old City of Jerusalem - the holiest site at which Jews can pray - in a mass prayer late on Sunday for their safe return.
- AAP