If I were you, I would keep with the potty training by asking your child if he needs to go potty but I wouldn't be as intense and focused about it as you are now. Just keep giving him opportunities but don't take it so seriously and don't get upset if he doesn't potty train quickly. Some children do it in a few days but others take months and months to really potty train. If you feel pressure yourself to make him perform well and he senses that pressure it can REALLY backfire on you and actually make the process a lot longer and much, much more frustrating.
It takes a LONG time for some children to potty train--especially boys. So, it's important to not set any type of time schedule like "My child will be potty trained in ____ amount of days/months." I think we started potty training with my son in earnest before he was 2-years-old (because he was going to nursery school at 2-years-old and we wanted him to be at least a little able to use the toilette there) but I would say he was finally truly potty trained during the daytime (he still wears pull-ups at night in case he has an accident) when he was about 2.5 or almost 3-years-old. He's almost 3.5 now. His grandparents had already been putting him on the potty and somewhat having him use the potty at their house since he was 3 months-old so he had A LOT of exposure to using the potty for a very long time before he really was ready to do it on his own on a consistent basis.
So, I think you can just relax and keep asking him as a normal part of the day "Do you need to go potty?" and then don't focus at all on the mistakes. (At this point, as you are just beginning with him--or at least that's how it seems from your post--I think it is actually inappropriate to really use any type of negative reinforcement--that puts way too much pressure on a child to perform. I really think the only time it's really appropriate to start doing this is if the child has been potty training for a LONG time--like 6 months-1 year and has shown that they are completely willing and able to use the toilette but then they choose not to do so--that is when you really start using small punishments. Punishment can be a recipe for disaster when potty training in the beginning, though.) But make sure that if he in any way does something positive toward potty training that you reward him with praise, stickers, snacks or anything else that he will enjoy. (Even willingness to sit on the toilette should be rewarded, I think as I know children who will scream and run away in terror at having to even SIT on the toilette).
It's also important to make potty training fun--so you need to associated it with a good time--not something he MUST do or he has failed. Some of the suggestions I have are decorating his potty with his favorite cartoon character or having an afternoon where you put the potty in the middle of the living room, strip him bare from the waist down and spend the day coloring, watching cartoons, singing songs, having snacks and doing fun things in the house. Have him drink lots of fluids--maybe his favorite fruit juice, milk or water so that he will have the urge to use the toilette and then just really focus on how "cool" it is to use the potty.
Keep asking him regularly (every 15-20 minutes--but don't ask too much) if he needs to go and if he does successfully give lots of praise and rewards and get really excited about it--celebrate his accomplishment--the look of excitement on your face is probably worth more than a lot of stickers! Eventually he will have the urge to go pee and because there are no underwear to get wet if he accidentally goes on the floor he can see the effects of what happens when you don't get to the potty in time. Then you can give him a towel, and in a non-condemning or punishing tone just say, "That's okay, you didn't make it to the potty in time. Next time you will. Now, we need to clean your pee up so you can help mommy do that."
We did this sort of activity with my son a couple of times and it really helped him get excited about potty training and made him much more eager to go on the potty. It takes patience and time but I think it's a good investment.
Just one more note--when my son really got involved in his own potty training was when he went to school (nursery school and kindergarten) and started to see other children using the toilette. Also, his grandparents have a good influence on this--encouraging him to be a "big boy" and go potty. Then my son made friends with a boy about 2 years older than him and noticed the boy used the toilette by himself at our house and after that he would say, "Mama, I don't need your help. Close the door. I can use the potty." So, peer pressure was very positive in this sense. But, notice, I never said to him, "Look, why can't you be like THOSE kids who use the potty by themselves?" He just noticed it by himself which I thought was really cool.
Good luck. Don't give up but also don't stress about it.