Chief Executive Fernando Chui Sai On says government department email accounts are among the hacked accounts provided by Companhia de Telecomunicações de Macau SARL (CTM).
Mr Chui said the government was concerned and would try to enforce cyber-security in all government departments, businesses and households.
Earlier this week, CTM said 34 of its Internet subscribers had been affected by suspected illegal cyber-activity.
The IP addresses of the hackers were traced to Hong Kong and the United States.
The Judiciary Police are investigating.