Party wants the Scottish Parliament to declare its support for the project and the oil and gas industry in general.
UK business secretary Kwasi Kwarteng has been advised of a potential claim for a judicial review.
Energy firm delays work at controversial Cambo oil field near Shetland amid protests by environmental group.
It comes after Nicola Sturgeon wrote to Boris Johnson asking him to 'reassess' oil and gas plans.
Nicola Sturgeon has written to Boris Johnson asking him to reassess the oil and gas plans.