Transporters want Cabinet Secretary James Macharia, the Kenya Ports Authority and the Kenya Railways restrained from forcing cargo owners to use the Standard Gauge Railway (SGR) or the old railway.
A five-judge bench was appointed to preside over a case in which some Mombasa residents are seeking to have the operations and management of the Kenya Ports Authority (KPA) handed over to the county government.
They say the directive issued by the KPA and the Kenya Revenue Authority (KRA) is in breach of the public trust bestowed upon them by the residents of Mombasa and is in violation of the Constitution.
The transporters want an order issued quashing the KPA and KRA directive and a declaration that Mr Macharia acted unlawfully and contrary to the Constitution.
The transporters' case comes as the High Court in Nairobi on Thursday temporarily suspended the government's directive on imported goods destined for three neighbouring landlocked countries.