Princess Haya was defending the FEI's new drugs policy, which allows low limits of certain anti-inflammatory drugs, identified in what is known as the progressive list.
The list, passed last month by the governing body's general assembly, ends the zero-tolerance policy in respect of several key medications, including phenylbutazone.
The decision has caused uproar among leading equestrian nations and leading vets have written to the FEI urging it to reconsider the new stance.
The German Equestrian Federation head, Breido Graf zu Rantzau, appeared to be talking last week of the possibility of European equestrian nations breaking away from the World Equestrian Games, but went on to stress that continuing under the FEI remained the top priority.
Princess Haya's defence of the new drugs position is outlined in a letter she wrote in reply to 15 leading vets, several of whom are currently serving in veterinary committee roles within the FEI.
The vets expressed their grave concern over the list and argued it had not been debated sufficiently.
"We believe a decision has been made that was premature, ill-considered and seriously retrograde. Permitting the use of NSAIDs will lead to abuse and the participation of horses in competition that are unfit to compete," said the vets, led by Leo Jeffcott, former chairman of the FEI Veterinary Committee.
However, Princess Haya, in her response, said one of the reasons the approach of the World Anti-Doping Agency is so successful is that there is naturally a debate as to whether substances are "performance enhancing" or "performance-restoring".
"It is however noteworthy that, while certain substances are the subject of debate, on the WADA list nonsteroidal anti-inflammatories are not considered to be problematic in human athletes," she said.
"In equestrian sport, the predominant argument in recent years justifying a complete ban on the use of these substances close to competition has been that the horse cannot choose for itself, and that therefore only such an approach can guarantee horse welfare.
"There are, however, arguments that, just as in human athletes, the use of NSAIDs [non-steroidal anti-inflammatory drugs] is acceptable to the extent it does not exceed certain levels (in humans, there is no limit), and is in fact more humane as it allows for very basic treatment close to competition that could be required to treat, for example, simple travel-related stiffness.
"There is also the argument that the banning of such substances is unrealistic as, since these are arguably a necessity, a ban creates a situation that does not allow for legitimate treatment by penalising it.
"I am inclined to support the latter arguments and brought them forward to the 2009 General Assembly in order to offer delegates a real choice.
"The voice of our member National Federations on this issue clearly demonstrates that there is not a universal belief that the use of such substances below defined limits is performance-enhancing, and that there is a significant body of opinion that permitting the use of certain substances, in certain cases with prescribed limits, is compatible with protecting horse welfare.
"The sport has clamoured for clarity on the issue of the difference between medication and doping, and a debate as to where exactly the line should be drawn can therefore be always expected.
"What is paramount is that policies and any changes thereto should be based on maintaining the health and well-being of horses through humane and strictly controlled veterinary practices.
"Imposing sanctions for the abuse of substances also provides a high deterrence value for the abuse of these controls.
"These were very much the considerations behind proposing two alternative lists which were put forward for a vote, aware of the compelling arguments for both. Horse welfare is and will continue to be my primary concern.
"By this vote the level playing field you refer to is maintained because the same regulations apply to all."
Princess Haya said the levels were advised by experienced national team veterinarians, including those of the United States and German teams.
"The intention is to allow a single subclinical treatment up to 12 hours before competition that would achieve a mild anti-inflammatory effect.
"... the intent under new regulations is to ensure that the treatment only takes place in supervised areas and with the oversight of the veterinary delegate."