The bureau confirmed that the first seven deaths resulted from complications arising from dehydration.
The causes of the deaths of the other five horses has yet to be advised.
The bureau said water in the area of the muster, which was postponed following the first seven fatalities, appeared scarce.
The bureau has the surviving 216 horses from the muster in holding facilities and is monitoring their health.
The Cloud Foundation said the bureau's contractor gathered 228 horses in less than 150 minutes over what it described as dangerous terrain.
The foundation's director, Ginger Kathrens, called for an immediate suspension of summer roundups.
"Tuscarora is another example of the bureau's reckless agenda," she said.
The foundation said it warned the bureau of the dangers of a July summer muster because of the heat and the dangers to foals, only weeks old at that time of year.
Its herd-watch programme director, Laura Leigh, who filed suit to stop the roundup in the Federal District Court in Reno, said: "This is what we feared and this is what we wanted to stop.
"The bureau's agenda absolutely disregards the welfare of these horses."
She continued: "More horses have paid with their lives due to the bureau's unwillingness to listen to the public and allow us to participate in management decisions and observation of our wild herds."
The foundation pointed out that current bureau plans aimed to remove 6000 wild horses in the next three months.