You don't mention what MTA you are using.
You don't mention what webserver you are using.
You don't mention what application (if any) your websites are using.
So now that you've given us nothing much to go on:
In general you should be able to add the user that apache runs under to an "approved sender" list and then check what your websites actually use to send mail. If you're using some form of off-the-shelf CMS or site framework it should be possible to set the originator e-mail through that.
Could try the following in the website .htaccess and see how you get on.
Code:
php_value sendmail_from -fxx@abc.com