The Democracy Movement and a team of attorneys representing a group of Cuban migrants found on a Florida Keys lighthouse filed an emergency motion Tuesday afternoon.

The injunction asks a federal judge to determine if the American Shoal Lighthouse is U.S. territory. The ruling is crucial for 19 Cuban migrants who on Friday climbed on the lighthouse about eight miles from shore near Sugarloaf Key.

All 19, and two others who didn't climb the lighthouse, are hoping to stay in the United States under the wet foot, dry foot policy. The Coast Guard negotiated with the group for several hours until they came down. They have since been in a Coast Guard cutter awaiting their fate.

"We're relying strongly on the 2005 precedent with the 7 Mile Bridge, we're pretty much making an analogy to this case and stating that just as the federal judge ruled in the 2006 case they should do the same with the lighthouse," attorney Virlenys Palma said.

"We have always defended the integrity of the territory of the United States and we believe that lighthouse is an integral part of this great nation," Democracy Movement's Ramon Saul Sanchez said.

Only six migrants are currently listed on the motion because they've been identified by relatives in South Florida. The others can be added later.

Coast Guard officials told NBC 6 Tuesday that all of the migrants are in good health aboard the cutter. They are given food and water daily.