Neural basis of primitive (newborn) reflexes The Wikipedia article on primitive reflexes, or newborn reflexes, states that they originate in the CNS. Here's the list of reflexes from the article:


Moro
Walking/stepping
Rooting
Sucking
Tonic neck
Palmar grasp
Plantar
Galant
Swimming
Babkin


Precisely where in the CNS do they originate?
It seems that there is not much research concerning the anatomical localization of primitive reflexes. For instance, Schott &amp; Rossor (2003) state in the conclusion of their review


  The complexity of
  many of these responses makes it perhaps unsurprising that
  detailed anatomical localisation, despite the availability of
  structural and functional imaging, has in general not been
  possible.


However, at least for the grasp reflex, they discuss an involvement of frontal areas. 

References
Schott, JM Rossor M (2003). The grasp and other primitive reflexes. J Neurol Neurosurg Psychiatry 74(5): 558–560. [DOI] [PDF]