Multiple RNA polymerases (RNAPs) transcribing a gene have been known to exhibit collective group behavior, causing the transcription elongation rate to increase with the rate of transcription initiation. Such behavior has long been believed to be driven by a physical interaction or ‘push’ between closely spaced RNAPs. However, recent studies have posited that RNAPs separated by longer distances may cooperate by modifying the DNA segment under transcription. Here, we present a theoretical model incorporating the mechanical coupling between RNAP translocation and the DNA torsional response. Using stochastic simulations, we demonstrate DNA supercoiling-mediated long-range cooperation between co-transcribing RNAPs. We find that inhibiting transcription initiation can slow down the already recruited RNAPs, in agreement with recent experimental observations, and predict that the average transcription elongation rate varies non-monotonically with the rate of transcription initiation. We further show that while RNAPs transcribing neighboring genes oriented in tandem can cooperate, those transcribing genes in divergent or convergent orientations can act antagonistically, and that such behavior holds over a large range of intergenic separations. Our model makes testable predictions, revealing how the mechanical interplay between RNAPs and the DNA they transcribe can govern transcriptional dynamics.