Mean square error (MSE) has been the preferred choice as loss function in the current deep neural network (DNN) based speech separation techniques. In this paper, we propose a new cost function with the aim of optimizing the extended short time objective intelligibility (ESTOI) measure. We focus on applications where low algorithmic latency ($\leq 10$ ms) is important. We use long short-term memory networks (LSTM) and evaluate our proposed approach on four sets of two-speaker mixtures from extended Danish hearing in noise (HINT) dataset. We show that the proposed loss function can offer improved or at par objective intelligibility (in terms of ESTOI) compared to an MSE optimized baseline while resulting in lower objective separation performance (in terms of the source to distortion ratio (SDR)). We then proceed to propose an approach where the network is first initialized with weights optimized for MSE criterion and then trained with the proposed ESTOI loss criterion. This approach mitigates some of the losses in objective separation performance while preserving the gains in objective intelligibility.