When he says "no, that he was sorry and that he would try to be on time" he is telling you there isn't really a reason for him being late. At least, nothing he thinks you can help him with.
Many workplaces have a flexible time schedule, but still have "core hours" which everybody should be present for. You could try implementing a similar rule.
He may not understand the importance of being on time. If he gets his work done, so what? That is where you need to explain to him why it is important. (assuming it is important). Since it sounds like you did that already, and he is still being late, maybe it still isn't important to him. What repercussions will this behavior have on him if he continues to be late? The answer to that question may be "important enough" for him to start showing up on time.
He could still have a legitimate issue - though if you follow the paragraph above and he still won't tell you why he has such a hard time then his issue could be something extremely personal (Depression comes to mind - can make it difficult to get out of bed). He may just not like the job, or the people he's working with. These would all affect his work performance as well. The problem with an issue like these is that he won't want to admit it and he may not even be aware of it, but so long as you ask if there is a problem and he says "no"... unless you see obvious signs that he needs help (Which means, you should recommend getting help. Or even push him to get help) there isn't much you can recommend or do about his problem - It may be he just isn't a good fit for the company.
I would just try letting him know the consequences of his actions first. You seem like you are understanding and want to work this out with him. He should see that as well. Just know you may end up having to fire him if the cost of his lateness is too high.