X2 begins several weeks after the first X-Men movie ends, in a world in which a new species of humanity has evolved within a very short time. These evolved humans, called mutants, possess special powers that cause many regular humans to fear them. There is ongoing discussion across all levels of society about the "mutant problem."

The movie opens with a group of tourists being led through the White House. One tourist strays from the group and is approached by a Secret Service agent, who asks if the man is lost. The man suddenly reveals himself as a mutant, attacks the agent, and starts fighting his way through security toward the Oval Office. This mutant has the power to teleport short distances (an ability known in the X-Men comics as "bamfing"), which allows him to easily evade the agents and reach the Oval Office...