Yes they generally will, but can charge around 5%
(according to this website )
http://www.tripadvisor.com/Travel-g293730-s601/Morocco:Banks.And.Money.html

Personally just use Visa Credit Cards there

For me my capitalone.com works great

Big Bank ATMs only usually local bank charge 3% or less.

ATMs are treated as cash withdrawals so always pay off quick

Do not travel with Debit card to risky for "skimming"

A good thief can clean you out...

People who create counterfeit ATM or debit cards by stealing your PIN and other account data can simply pull cold cash from your bank account. Using a technique known as skimming, they set up equipment that captures magnetic stripe and keypad information when you input your PIN at ATM machines, gas pumps, restaurants, or retailers.

Caveat Emptor!

Just an advice about ATM's using in Morocco. you'd be better if you use BMCE Bank,this is one that is adviced to use in any case. because it's special for overseas and commerce.
Others are sometimes been created for locals, so they could make some problem, or could refuse your card. Moreover; try to use Visa which could be accepted wherever you use it.
for more details about his try to check out the link that Nikao has suggested because on Tripadvisor there is a link special for Bank and currency etc...
Have a good travel.

I have drawn from my debit card in Marrakech & Essouria and it was fine, but I had to go to 2 ATM's to get this right - but generally speaking you should have no problem drawing money and it does work out cheaper (and quicker) than going into the bank to exchange.

Thanks for your replies.

As I am in Morocco now, I do see a $3 charge on my account when redrawing 4000 dirhams. I am not sure whether this charge comes from the banks I used-> BCME and Bank Populaire or my home USA bank. I will eventually find out.

But considering the amount withdrawn, the charge seems reasonable. I do try and use BCME when ever I can.

Thanks for your input and warnings.

G

You are Most welcome, have a good time in morocco.