Can´t send invite emails though test emails work

I just set up an instance of mattermost 2.2 on a private vps. I entered my email credentials and sent myself a test email. Everything worked fine. But when trying to send an invitation to team members I get the following error in the console:
[2016/05/16 18:25:05 UTC] [EROR] Failed to send invite email successfully err=SendMail: , 554 5.7.1 Relay access denied
I also tried with a gmail address but had the same problem.
Does anyone know a solution?
Thanks a lot!

Hi @skip-sands,

Can you share a sanitized copy of your SMTP settings? That will help me diagnose your issue.