It's ambiguous. Grammatically either man could be meant:

- Most readers will take "he" to refer to the subject (the doctor) — i.e. the doctor phoned to say he would be late.  
- It can also mean the nurse was late (the doctor phoned because the nurse was late).

To remove the ambiguity, rephrase: e.g. "The doctor phoned the nurse to say he would be late" (doctor) or "The doctor phoned because the nurse was late" (nurse).
