Within the core .net core, you cannot stand right now.
At the time of writing .net core version 1.1, the .net 1.6 standard is being implemented. At that moment, System.Net.Mail was not migrated. But, as you can see by this request: https://github.com/dotnet/corefx/pull/12416 . It looks like he's going to turn it into .net Standard 2.0 (which is likely to be implemented in the next version of the .net kernel).
At the same time, it seems that everyone is using the MailKit library ( https://github.com/jstedfast/MailKit ), which works very well!
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