Right now, even after the court decision, there is what amounts to a standoff. This month, the federal government said it was willing to allow more 55-gallon drums on main pathways in the refuge. It said it would not permit any gallon jugs.

But the water jugs continue to appear.

Last week, Gene Lefebvre, a retired minister who co-founded No More Deaths, hiked along a path popular among immigrants until he reached a clearing where volunteers for his organization had recently left some jugs.

Each bottle had markings on it noting the date it was left and the exact location on the group’s GPS mapping software. There were also signs of encouragement for the immigrants: a heart and a cross on one bottle and the words, “Good luck, friends,” on another.

“We’d give water to anyone we found in the desert, even the Border Patrol,” Mr. Lefebvre said.

But opponents say the water drops are encouraging immigrants to continue to come across the border illegally. The critics say there ought to be Border Patrol agents stationed near the water stations to arrest those who are crossing illegally as soon as they finish drinking. So furious are some at the practice of aiding immigrants that they have slashed open the water jugs, crushed them with their vehicles or simply poured the water into the desert.