A hot topic recently attracted much interest in 3GPP community is ultra reliable low latency communications. While specific protocols for such type of communications are under development, in this paper we evaluate how well we can meet strict quality of service requirements in the current LTE/LTE-Advanced networks. Specifically, we design a new two-step radio resource management algorithm for reliable low latency communications. At the first step, the algorithm forms a high-priority group of users which can be reliably served within the given delay budget. At the second step, the algorithm solves a linear optimization problem and allocates resource blocks to meet quality of service requirements at least for the users from the high-priority group. With simulations, we show that the proposed algorithm outperforms existing ones in terms of goodput, PLR and the number of satisfied users.