Thousands of troops searching for the youths turned their attention overnight to the northern West Bank city of Nablus and surrounding area, arresting 41 Palestinians, the army said.
So far, Israel has arrested around 200 people, most of them Hamas members, as it presses a vast search operation for the students, two of them minors.
Prime Minister Benjamin Netanyahu has accused Hamas militants of kidnapping the youths last week, but has warned that the hunt for them "may take time."
So far, there has been no formal claim of responsibility, and Hamas has dismissed Israel's accusations as "stupid."
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Yesterday, the European Union condemned "in the strongest terms the abduction of three Israeli students" calling for their immediate release.
"It is, frankly, despicable that children's lives should be put in danger in this way," Lars Faaborg-Andersen, the EU's ambassador to Israel, said in a statement.
"As long as our boys remain abducted, Hamas will feel pursued, paralysed and threatened," said Lieutenant Colonel Peter Lerner, the military's official spokesman.
"We are committed to resolving the kidnapping and debilitating Hamas terrorist capacities, its infrastructure and its recruiting institutions," he said.
Ministers also examined the possibility of banishing its senior members to Gaza and demolishing their West Bank homes, media reports said.
Meeting again today for three hours, the security cabinet decided to further "increase pressure" on Hamas, an official told AFP, saying there was "a discussion about steps that can be taken against Hamas prisoners."