Information adviser Zahid ur Rahman said legal action could be taken against those who broadcast former prime minister Sheikh Hasina's remarks in breach of a court directive.
He made the comments on Tuesday at a press briefing at the Secretariat.
Rahman said that if Hasina, who is abroad, delivers a statement on August 5, its distribution through media or other channels would amount to a violation of the order.
He said the government has a constitutional duty to implement court orders.
Rahman said the government was not itself a court and that anyone opposing the restriction could seek a legal challenge to the order.
He said individuals and institutions were required to comply while the order remained in force.
The adviser said relevant media organisations and institutions would again be cautioned and given necessary instructions.
He said a warning had previously been issued over the matter.
Rahman also said the government wanted to bring Hasina back to the country to face legal process and would ensure her legal rights.