Sending large volume of account activation emails without getting blocked?

A white ago, I had to develop a website for a company. It reqires account registration, activation, then logging into the system to fill a form, ect. This was proposed to reduce spam and fake data entry.

What I did not expect is that: within 5 days I got over 16,000 account registered (only about 8000 was actual users). Sending activation email started to fail soon after the site started due to the email account being blocked as a result of high volume of emails.

I checked amazon simple email service and they only offer 200 email to be send by day. I asked them raising the email limit to 5000 per day, but my query was refused.

I had to cancel the activation process in the end. My question is: what is the best way to send very large volume emails (for account activation). Also is there another way to do it to avoid email issues?

Any advice is highly appreciated