I've never checked to see if the mktime() can do it... what I have done in the past is the following:
Make an array with the months in it, but leave the first key blank, so...
$months = array('', 'January', 'February', 'March', 'April');
etc
Then you can strip off the two characters for the month from your timestamp using substr() and write that as a new variable (let's say $the_month).
Then just echo your date out and echo the month by doing:
echo $months[$the_month];
mktime() might be a little quicker in processing if it can in fact do it... but the above method has worked fine for me in the past.