Both Iago and Othello could arguably be cited as responsible for Desdemona's murder.
Othello actually committed the crime of murder when he suffocated his wife. If responsibility alone lies in the physical hand that committed the act, Othello is the man. He will admit to it.
Iago on the other hand, manipulated Othello with lies and half-truths throughout the play which produced the emotions and urges within Othello to carry out the action. Emilia questioned Iago on the lies he told Othello and Iago confessed his crime to Emilia. Emilia blames Desdemona's death on Iago. Iago orchestrated the events that led Othello to kill his wife. In my opinion, Iago is responsible for Desdemona's death.