A method to treat cancer and other malignant diseases, said method comprising parenterally administering an agent which destroys blood extracellular DNA into the systemic circulation of a cancer patient to slow down cancer growth. The agent is embodied in the form of a DNase enzyme and, more particularly, as a DNase I enzyme. Doses from 50,000-250,000,000 Kunitz units/day are administered for 5-360 days.