I want the K2 Item edit menu should open with parent window. However, K2 Item edit menu automatically opens with new window. Changing the target window value isn't working. It automatically sets the value - 'new window with navigation'.

I am using Joomla 3 and k2 2.6.9

Unfortunately this is how K2 works.
The edit/ add item form opens in a new window or a modal.

You can create a override and remove the modal class (there is a thread in the forum about this) but it might lead to unexpected behaviour.