How to deal with people who don’t respect my turn to speak in a conference and interrupt me many times?

I have to colleges in different departments who are so difficult to deal with when I have a conference with them. Both act the same way, they don’t let me finish my speech and sometimes interrupt me in a moment where if I stop talking all what I’ve told won’t make sense or will sound like something different than what I actually mean.

For example in the last conference I’ve tried to defend my department explaining the whole problem that affects our department and others and when I was assuming our part of the blame talking about our mistake and the way to fix it, a girl of another department which is also involved interrupted me saying “Exactly that’s your mistake” almost screaming and she continued talking about it for a minute. Then the conversation turns around our mistakes and not about the real problem leaving us as the guilty ones.

They also use this strategy speaking louder than me when they want to interrupt me.

Any idea to deal with them?