It's best right now to give him time, he is angry right now because he felt he had to pay for what every other guy put you through and he blames you for the break up. If you push now you may never have another chance with him. Try to be his friend for now and gain his trust again he thinks if he gives you another chance it will be pretty much the same thing all over again show him that you have matured and if that means giving yourself time to get over past hurts then that is in your best interest because if he gives you another chance make sure you don't have any emotional baggage this time so that you can both start fresh.
It's easier for him to be angry with you and not show his true feelings this may be why he said he had a girlfriend when he didn't have one, he is finding excuses to get over you and hurt you as much as he felt you hurt him. What you should do since you live far away, sit down and think of what you want to say to him and write it in a letter, explain to him that you were wrong for treating him the way you did and that you want to at least be friend if you cannot be lovers but you hope that one day he can forgive you enough to give you another chance at love with him because you cannot see yourself with anyone else. Something to that affect to show him that you really do care and want him back.
The saying goes "Time heals all wounds" maybe that is what you both need right now, you time to heal old wounds from past relationships and him time to heal from the hurt of the break up. I would write the letter and send it to him and tell him at the end of the letter that you are giving him time to think about what you've wrote and then give him just that and while you are giving him time write down everything bad that has happened to you in past relationships and then work on those things so that they don't happen again if he does give you another chance.