I listen a lot to local and DX AM radio. Your situation sounds like a major FCC violation. Something in that router is defective if it's transmitting wide-band spurious noise into the kHz band. It's time for a replacement.
If the noise stops when you pull the power from the router, then it's at fault and you need a replacement.
If the noise stops when you pull the power from the router, then it's at fault and you need a replacement.