You can ask them to send a notice by email to everybody to provide this. Do this through your manager. Maybe it could be escalated to senior levels.
Secondly - do not use official email for any form of personal discussion with anyone. If you have done so already, please delete it immediately.
Hope this helps.
I echo Ryan and request you to explain why would the IT Department need the passwords ? Which password is they asking for? Is it the login password to the laptop/desktop or to the mailbox ?
They anyhow have an access to each and every interaction within their network, including intranet and mail boxes.
Asking for the password separately rather looks like an initiative to forewarn employees on their interactions.
Please try and understand why the system have been set . Sharing password is against the Code of Conduct to every firm.
Looking forward to hear from you!
If password is to be shared for any reason, it should be well documented and notified to stakeholder to avoid any dispute later on.
You should also confirm incase your Email account is misused, how responsibilities will be fixed. (Rare chance but still a Grey Area).
Ppl can misuse the profiles...
IT employees anyways have the accesses to all accounts and may create or delete the profiles. Also like you already said it is asked verbally so please do not take any action.
In case if someone really pressurize you please share a wrong password ;)
Hope it helps!!