Presently I've my Facebook profile instantly publish blogs from the WordPress instance.

What I must have the ability to do, however, would be to also provide comments published either to your blog of Facebook show on another within the appropriate location.

It is possible to method of doing this using the Facebook API?

There's a lot of facebook-connect enabled WordPress plug ins that can help you accomplish this. Here is a couple:

yoavf response is good. A listing including individuals plug ins is maintained in Facebook's wiki: http://wiki.designers.facebook.com/index.php/Facebook_Connect_Wordpress plugin_Directory

http://dentedreality.com.au/2008/12/applying-facebook-connect-on-wordpress-in-reality includes a novel approach that is not on that list.

you have to visit the supply of your blog, work out how the comment form is published (Publish or GET) you'll be able to use mock ajax documentation here. then within the facebook application, you develop a form like the one for that blog comment. make certain all of the ids from the particular form elements are the same. after that time your submit button you've got a link such as this.

<a  clickrewriteid="dummy" clickrewriteform="comment_form"

clickrewriteurl="blog_form_action">Submit</a>

so dummy may be the id of the element which will recieve any output.
comment_form may be the id from the form that'll be published towards the blog comment processor.
blog_form_action may be the url inside your blogs form action attribute.

if things work, the shape comment_form is going to be published for your blogs processor page to ensure that the comment posted from facebook can look around the blog too.

when the blog uses GET since it's method, you simply make certain that blog_form_action consists of the query string

hope that can help!