ULAN BATOR, Mongolia — Defense Secretary Chuck Hagel knew even before he landed here that there was no way he could keep the horse.

In the vastness of landlocked Mongolia’s steppes, horses have always been a big deal, and when Mr. Hagel’s predecessor, Donald H. Rumsfeld, made the first visit to the country by an American secretary of defense in 2005, his hosts honored him with the traditional gift of a horse. Mr. Rumsfeld named the black-maned gelding Montana, because the landscape reminded him of the state where his wife, Joyce, was born.

But along with Montana came some delicate issues of diplomacy, logistics and politics, not the least of which was whether American taxpayers would have to bear the cost of upkeep. After a great deal of head scratching, Mr. Rumsfeld ultimately had to leave Montana behind, to be watched over by the horse’s herder, the Defense Department said, “until his next visit.”

When President George W. Bush followed Mr. Rumsfeld to Mongolia a short time later, the White House quietly persuaded Mongolian officials not to give the president a horse, and they complied. Mr. Bush did partake in Mongolian horse culture another way, by drinking the local brew, fermented mare’s milk.