The invention relates to medicine and concerns a method for the poly signal activation of apoptosis of malignant solid tumour cells, carried out by means of the targeted delivery of thallium salts by surface-modified MS2 phage virions which contain a cyclic iRGD ligand that has a high affinity for the integrins avb3 and avb5 and is covalently bound with the shell and with the core, which contains genomic RNA and thallium salts. The invention provides for complex, efficient, prolonged cytotoxic action on focal and metastatic clusters of malignant solid tumour cells, while minimizing undesirable side effects on the healthy cells of an organism.