What Would Cause A Pus Discharge From My Dog's Penis?

You need to take your dog be seen by a veterinarian.  This could be related to an infection in the bladder, penis, or prepuce.  Bladder stones are also possible.  The penis and prepuce also could have a mass present or a foreign body causing the problems.  
Your dog needs his condition diagnosed and needs to be started on antibiotics and pain medication.

Is this your first male dog? I ask because male dogs do tend to discharge fluid from their penis from time to time that does look like pus, but in fact is quite normal for them to do this.

I have three spayed male dogs who are with me all the time, and have never witnessed either of the symptoms you describe. It may be that they are all just extremely fastidious about their hygiene, but I think it's more likely that your dog has some kind of an infection or irritation going on.
I strongly urge you to at least speak to a vet about it.

As long as it is emitting foul smell out of it, there is no need to get worried about the situation. This is just a normal discharge that is smegma having dead epithelial cells. It comes out of Mucoid Glycoproteins and many dogs go through it in their lives. If there is inflammation as well or itching is there then you should take it to vet for checkup.

I have The same exact problem!! I have to mop The floor like 3 time a day.  I have limited my dog to one area of the house because I see the drops of pus all over the floor and when it gets dry, its so difficult to clean.  Does anyone know the name of the antibiotic or medication for this??

My dog has the same problem...you can't get rid of it all the way.50% will go away when you fix him...and as for the swelling its cause his penis is always hanging out and it gets dirty so the head gets swollen and you have to take sugar put it in warm water and then massage it around his penis.yup thats what I have been doing for the past 3 years.I am 100% lesbian and ive touched more penis with this dog then I have in my whole life...lol but n e ways thats what the vet told me to do and its been working just for the swelling though.you can't stop the green stuff from dropping..

My dog has puss in his eyes and coming out of his penis ?

It is very important to check the female before you get your dog mate.This can cause infections and other diseases if not vaccinated before matting.