Yes, so long as the landlord is not conditioning your acceptance of the money on your agreement that it is payment in full. He may do so in a cover letter he sent you, or he may do so by writing "paid in full" or something similar on the check.
If he is placing such a condition on your acceptance of the money, then legally he has not paid you anything at all. Return the check and sue him for the full security deposit.
Yes you can sue, assuming the check for $600 is not conditional (such as with a notation "paid in full").
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This Avvo.com posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult with your own attorney.