Portions of the US government have tried multiple times to make the addition of backdoors required via public force of law. They're still trying to promote it now. Short of that public requirement, they can ask & issue orders to not discuss the matter, tie it with defense orders, or imply the withholding of export or trade licenses, all contingent upon cooperation. In the end it looks pretty blurry between a request for cooperation and and order.

Even in China, they might not need to rely on explicit state security authority, just tie it up with state sponsored funding or other softer measures.