I find the concept in multiple areas in the TaNaKh.I agree, the directive to be righteous can be found in Tanach. But the method is completely new. Being born anew and receiving the Holy Spirit are innovations brought by Jesus.
This ^^ is a new law. Not Jewish.
This is a completely new concept, Not Jewish.
Whether a new heart (Ezekiel 36:26), a new name (Genesis 32:28), the new beginning in the promised land (Joshua 4) , placing His Spirit in you (Ezekiel 37:14)
Maybe he was just bringing understanding of the same?