A coalition of environmental groups will soon start knocking on doors in Congress, hoping to change a 147-year old mining law that has withstood earlier attempts to revise it.

The groups are looking to 2021 at the earliest to make changes, using the time until then to explain their plan. They want to impose royalties on minerals extracted as well as environmental regulations—both of which the General Mining Law of 1872 doesn’t contain—and establish a fund for cleaning up abandoned mine lands.

“Our hope is that, by doing it this year, we get to do this education over a...