In the K2 item comment template, a test can be added to check if the user is logged in.

If not, no form but a link to a login/register page

Modifications have to be made in components/com_k2/templates/default/item_comment_form.php

Between the h3 and the form element in:

<?php

$user = & JFactory::getUser();

if ($user->guest): ?>

<a href="index.php?option=com_user&view=register">New Visitors, Register to Comment</a>, or members can 
<a href="index.php?option=com_user&view=login">Login</a>

<?php else: ?>

And at the end, after the closing form add:

<?php endif; ?>