Earlier answers pointed out that this question is based on a mistake about general relativity, in which gravity neither pushes nor pulls: but it is also based on a mistake about Newton's view and about what he wrote. Newton was emphatic in refusing to commit himself to identify gravitational attraction either as a push or as a pull. He said he was concerned only with the mathematical quantities and relations of the forces, etc. He wrote that he used the words 'attraction' and 'impulse' indifferently, 'one for another' in respect of the general propensity of massive bodies to approach each other, and he expressly abstained from speculation about their physical nature or cause (see quotations below).
Accordingly, just as the other answers point out that GRT does not specify gravitation as either a push or a pull, neither did Newton's physics. Whether in GRT or in Newtonian physics, the answer 'push' or 'pull' is unnecessary to an account of the physics. The question in effect poses a false antithesis.
Here is the basis so far as what Newton wrote. In the opening parts of the 'Principia', in Definition VIII, Newton wrote (quoted here from the 1729 English translation of his original Latin, available online at https://books.google.com/books?id=Tm0FAAAAQAAJ):
"I ... use the words Attraction, Impulse or Propensity of any sort towards a centre, promiscuously, and indifferently, one for another; considering those forces not Physically but Mathematically : Wherefore, the reader is not to imagine, that by those words, I any where take upon me to define the kind, or the manner of any Action, the causes or the physical reason thereof, or that I attribute Forces, in a true and Physical sense, to certain centres (which are only Mathematical points) ..."
In the same vein, his Definition V stated that "a centripetal force is that by which bodies are drawn or impelled, or any way tend, towards a point as to a centre".
Later on he emphasised yet again the same abstention from speculation (Principia, Book 1, Section XI, Scholium following Proposition 69):
"I here use the word attraction in general for any endeavour, of what kind soever, made by bodies to approach to each other; whether that endeavour arise from the action of the bodies themselves as tending mutually to, or agitating each other by spirits emitted; or whether it arises from the action of the aether or of the air, or of any medium whatsoever, whether corporeal or incorporeal, any how impelling bodies placed therein towards each other. In the same general sense I use the word impulse, not defining in this treatise the species or physical qualities of forces, but investigating the quantities and mathematical proportions of them; as I observed before in the definitions."