The output stabilization problem for a linear system with an unknown bounded time-varying input delay is considered. The interval observation technique is applied in order to obtain guaranteed interval estimate of the system state. The procedure of the interval observer synthesis uses lower and upper estimates of the unknown delay and requires to solve a special Silvester's equation. The interval predictor is introduced in order to design a linear stabilizing feedback. The control design procedure is based on Linear Matrix Inequalities (LMI). The theoretical results are supported by numerical simulations and compared with a control design scheme based on a Luenberger-like observer.