Yes there are two ways we do it.
1) Create a custom email provider and then create the link and code and send it to whomever you wish. If you wanted to get snazzy with it, you could set up a setting in the Settings module that you could add an email(s) into and that the Custom Email Provider Class could read from, so it isn't all hard coded. They will click the email and it will approve the account when the page loads.
2) Create a custom email provider and then expose a rest api, so when they click the link it is sent to the api which confirms the account. We use this for mobile and sms text.
The first one is the easier of the two. It shouldn't take you more than 30 minutes or so to do this if you can write C#. See the example in documents, "Custom Email Provider".
Additionally you indicate "Approve" or "Reject". If you are requiring Approval than each new user is, in fact, in a rejected sort of state. If by "Reject" you want to delete or somehow flag the user in another way, then you will have to write some custom code to do something and/or us API-REST.