Should I go after him?

We've been talking with a guy for a long time now and we also spent time together a few times and hooked up several times. He acts interested and before he was also saying that he likes me a lot, but I think I pushed him away a bit because I was acting odd - I was making claims when I really didn't have the right to do it as we're not dating. The thing is, I like him so much it's crazy. I realise there can't be anything serious between us because he leaves soon and we're living in different countries. I apologized to him for being too pushy and he said he never thought I was aggressive or something. At the same time, I know there is another girl he saw recently, but nothing happened between them just yet.

The thing is that even though he is acting interested, he said he likes me and he's all over me every time we meet, he never takes initiative. And because of that, I am always confused about how he actually feels about me. So, my question is, should I approach him again? I am afraid that if I suggest to meet he will think that I am being pushy again. also the situation with him seeing another girl strains me as well.
Should I go after him?
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