Gamma-Ray Bursts (GRBs) have been traditionally divided into two categories: “short” and “long” with durations less than and greater than two seconds, respectively. However, there is a lot of literature (with conflicting results) regarding the existence of a third intermediate class. To investigate this issue, we carry out a two-dimensional classification using the GRB hardness and duration, and also incorporating the uncertainties in both the variables, by using an extension of Gaussian Mixture Model called Extreme Deconvolution (XDGMM). We carry out this analysis on datasets from two detectors, viz. BATSE and Fermi-GBM. We consider the duration and hardness features in log-scale for each of these datasets and determine the best-fit parameters using XDGMM. This is followed by information theory criterion-based tests (AIC and BIC) to determine the optimum number of classes. For BATSE, we find that both AIC and BIC show preference for two components with close to decisive and decisive significance, respectively. For Fermi-GBM, AIC shows preference for three components with decisive significance, whereas BIC does not find any significant difference between two and three components. Our analysis codes have been made publicly available. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.