Gain eye contact before you start talking. Maintain that eye contact. Looking away breaks the communication link with the other person.
“Maintaining eye contact may sound easy. For many people it is very hard. I know stutterers who have gone through various therapies with some success but who still have been unable to break their old habit of looking away from their listener when a block begins.” – Murray
The Stuttering Foundation says to start by looking at yourself in the mirror and keep eye contact with yourself. Then look at yourself in the mirror while making some phone calls. Concentrate on looking at others even when they look away if you start stuttering.