In the brain-computer interface based on the P300 wave (P300 BCI), the selection of the command by the user becomes possible due to focusing the user's attention on the external stimulus/command and extraction of the response to this stimulus in the form of the event-related potential (ERP) components from EEG. To obtain the ERP signal, stimuli should be repeated many times, however, in view of the existing variability in latency of the response to certain stimuli, the averaged ERPs may give a distorted view of the nature of such responses and reduce accuracy of the interface. The study was aimed to develop an effective method for identification of the effects of the ERP components' latency variability and for accounting these effects in the P300 BCI, as well as to identify the possible impact of psychophysiological factors on the nature of ERP variability. We have conducted a BCI-based study of 19 healthy subjects involving extraction and adjustment of latency in the N1 and P300 spatial components, which play a key role in the command classification in the P300 BCI, to explore the mechanisms underlying variability. Such an approach ensured higher accuracy compared to the use of conventional EEG leads, and the highest increase of 10% was observed when using the minimum number of the stimulus repetitions. Furthermore, modifications of the interface allowing one to ensure a higher level of the user's focus on the task and a more accurate visual fixation on the target objects contributed to the increase in the amplitude of the ERP components  by reducing variability of the responses to single stimuli. The findings emphasize the important role of the processes underlying the ERP components' variability and provide an effective tool for scientific exploration of such processes and the development of advanced BCI systems.