Or
on a hacked phone

There might be another term for this sort of phone monitoring, but this is what comes to mind. Examples are at the link.

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Note added at 22 mins (2013-03-25 16:48:10 GMT)
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Good example of the English phrase in this context at the first result on my linked list of examples:

"Whichever way you choose to purchase, buying precious metals from Monex is quick, easy and secure. Once you have decided on what and how much to purchase, your Account Representative will assist you in executing your order over the phone, and your purchase and price will be confirmed on a tape recorded line after your acknowledgment. A written confirmation of your purchase will then be mailed to you by the next business day." – http://www.monex.com/why/howtobuy.html

At the start of a call to a company, I am often told that the call will be recorded. So, it is the call that is recorded rather than the line, if that makes sense. I would change the sentence slightly to allow for the difference in expression between Norwegian and English, rather than follow the original sentence structure slavishly.

...that he would call me on a recorded line...

Oh boy. There are so many methods for listening in on a conversation. Tapped it not far from being correct, but wiretapping refers to a specific set of methods, intercepting inline signals between the phones. Tape recorded is too specific, sorry to say, as that happens when the conversation in done over the speaker phone, and besides, aren't MP3 recorders more popular?
A monitored line simply means the signals are being observed by a third party or device. This can include coil induction, electrical wiretapping, dial registers, audio recordings on a speaker phone, or other specialized equipment.