In Act 2, Scene 3, Artemidorus reads his letter aloud in order that the audience will know exactly what warnings it contains. The letter warns Caesar against Brutus, Cassius, Cinna, Trebonius, Metellus Cimber, Decius Brutus, and Caius Ligarius. Then in Act 3, Scene 1, Caesar apparently accepts the letter but refuses to read it immediately, as Artemidorus is urging:
O Caesar, read mine first, for mine's a suit
That touches Caesar nearer. Read it, great Caesar.
Caesar takes advantage of the opportunity to showcase his great altruism and personal humility:
What touches us ourself shall be last served.
It would seem that Artemidorus is as insistent as he could be under the circumstances. He can hardly get to Caesar with all the conspirators surrounding him. He does not know for certain that they intend to kill Caesar at that very moment, and perhaps there is nothing Caesar could do to save himself if he did read the letter immediately. He is not armed, and he is surrounded by desperate enemies who are armed with swords and daggers.
It is ironic that we all know Caesar is bound to die because it actually happened in history on the Ides of March. Shakespeare creates an illusion that the audience has traveled back in time and is witnessing the actual event.