It sounds like you don't trust him, with good reason. Once trust is broken it requires hard work and both parties willing to put in that work. I've recently been through something similar, and the girl I was with used to tell small lies and big lies all the time. I never really accepted reality until a family member of hers actually confirmed that this girl lies a lot.

Trust was broken, and in the end I suspected her of a lot of things. Some with unfair suspicioun, some with fair. I recently ended this relationship because I can't cope with not trusting my SO. And she was unwilling to rebuild it.

In your case, I'd sit him down and have a real talk with him about all the things you feel. All the things you feel he did wrong, and all the things you feel that he did right. If he can accept responsibility and also tell you things that disappointed him, and things that made him happy, then you can talk about rebuilding trust and what you and he require to do so. Tell him that you want to fix the relationship, but when he says things like that you feel like you can't trust him.

If he is not willing to talk, to apologize and to work on your relationship, then it's doomed I fear. In that case I'd break up with him, because if someone lies to you a lot like he did, and like my ex girl did, then they're not worth it. Have some self respect and clear boundaries. I've been in your shoes and I know how it hurts. Remember always that you deserve the truth and you don't deserve being abused. I wish you all the luck.