WordPress not sending E-Mails (but SendMail is running)

I am running WordPress 4 Multisite on Amazon Linux (RHEL Linux) with SendMail installed.
I have verified that the php.ini points to SendMail and SendMail is actually running ("sudo service sendmail restart").

When trying to send E-Mails from WordPress (either by requesting a Password Reset mail or sending MarketPress order confirmations), emails are not being sent.

When trying to send a Password Reset mail (to test the WordPress email service), I get the error message: "The e-mail could not be sent.
Possible reason: your host may have disabled the mail() function."

What else could I try to fix this issue?

Thank you!