Interval arithmetic has been widely used for power systems analysis considering uncertainties associated with load and generation data. However, little work can be found within the context of three-phase distribution systems due to their peculiarities such as radial topology and unbalanced loads. In this paper, a novel methodology is proposed for determining interval results of a power system load flow for three-phase unbalanced distribution networks based on the Three-Phase Current Injection Method (TPCIM) in which state variables are considered in rectangular coordinates. In the proposed approach, active and reactive powers at each load bus are modelled as interval values to represent their inherent uncertainties and the Krawczyk operator is applied into the power flow equations in order to provide reliable interval three-phase results. Additionally, the use of interval extensions and an angular rotation technique are proposed to overcome overestimation problems associated with the interval solutions. Computational simulations are carried out using IEEE 13, 33 and 69-bus test systems. The main contribution of this work is the proposition of two methods based on traditional interval arithmetic to reduce the diameter of the solution and achieve similar results when compared with Affine Arithmetic and Monte Carlo Simulations. Additionally, the computational time associated with the algorithm is extremely advantageous. The method is useful for power distribution systems operation and planning studies, representing a viable and useful tool for calculating the impact of uncertain input data on the power flow results.