Is Buddhism antinatalist?

I was listening to a discussion with David Benatar, and the point that Buddhism seems to be antinatalist was raised. It seems that people argue this both ways. Can Buddhism be said to be antinatalist? Or some strands but not others? If it is, what consequences does this have? I have always kind of dismissed Benatar's ideas as being a kind of Larkin-esque pose, and making a mistake in hierarchy that puts pleasure above meaning, like utilitarians. But if the charge of antinatalism sticks, it seems I am going to have look more carefully at which of his points also apply to Buddhism.