Weizman told reporters that extensive coverage of the case, which has strained Israeli-Egyptian relations, had not helped resolve the problem.
Netanyahu said earlier this month that he expected Mubarak to pardon the 35-year-old Druze man.
Mubarak later rebuffed the request, saying that Netanyahu had insulted the Egyptian judicial system when he called the verdict in the case “twisted.”
Azam, a mechanic at an Israeli-Egyptian textile plant in Cairo, was convicted Aug. 31 of spying for Israel and sentenced to 15 years in prison with hard labor.