Hi Ali,
this was one of those symptoms that I got the message was really interpreted critically by others so I practiced and challenged myself to overcome it. It still presents itself in situations where I'm faced with an attractive person of the female persuasion or an aggressive adversary.
I had to practice spontaneously on the weekend as part of our church service was to turn to the person next to you and chant some spiritual dialogue. I broke the tension by looking away occassionally.
It is one of those skills that can be learned and then is very personal. If I stare too intently at someone, that can be misinterpreted, so there needs to be a gentle balance.
I've been told by some people that I don't look into both eyes at once, which I imagine is true. I'll look into one eye or at the face generally. Looking directly into both eyes is pretty advanced and awfully intimate.