If he has had a bad experience with going outside, then he won't want to go back out again. Use lots of treats and praise when you put his leash on, lots of praise and playing when you get him outside, and then you wait.. and wait, and wait, and wait. You literally cannot bring him inside until he goes. If it's been an hour (which has actually happened to me before) then take him back in and put him immediately into his crate. You might even want to keep his crate right by the door, so he doesn't get a chance to pee on the doormat. Wait about 30 minutes and then take him back outside. He will eventually realize that this is his one chance to go, or he will have to be stuck in his crate holding it or pee on himself, which is a miserable experience. After about a week of that, he'll start going to the bathroom when you take him out to go.
When my dog was a pup, she knew she was going into her crate after, but she also knew I would stand there and wait until she did her business, so she started seeing just how long she could run around before I'd call it and take her in. I would stand out there while she sniffed around for ages, but as soon as I called her and told her it was time to go in, she would "magically" find the perfect spot and use the bathroom right before we went in.
To get the leash on your pup crouch down to his level normally it will entice the puppy to come towards you. With my puppy he didnt want to go outside either. I used a leash and stood in one spot. They do get bored eventually and will use the bathroom then praised accordingly!