Secretary of State James A. Baker III's planned visit this week to Mongolia, a country low on the list of U.S. diplomatic priorities, has caused grumbling within the State Department, where some officials say they believe diplomacy has been fashioned to suit Baker's sporting needs.

The visit, and the grumbling, began with a Mongolian invitation last fall for Baker to stop in that country. Mongolian officials also held out the opportunity for Baker, an enthusiastic hunter, to try to shoot an exotic argali sheep, according to government and private sources.

A threatened species, the argali sports curled horns that can grow to six feet. It is the largest wild sheep, and its mounted head is considered a major trophy, particularly among Texas sportsmen who hunt animals around the world.

Yesterday, in response to a query from The Washington Post, Baker spokesman Margaret Tutwiler, who is traveling with him, said that Baker has no intention of hunting the argali. Instead, Tutwiler said, Baker will take time off on his last days in Mongolia this Friday and Saturday for fishing and perhaps hunting "wild goats {that} are not on any threatened lists" and are "like hunting deer in Alabama."

"He would not ever hunt something that was endangered or threatened or about to be on those lists," Tutwiler said.

A State Department official said yesterday that Baker might "try to see an argali, but he won't shoot it."

In the State Department, where the trip has become something of a cause celebre, diplomatic sources question Tutwiler's account of when and why Baker decided not to hunt the argali. Rumors have swirled within the department about the killing of endangered species and the expenditure of hard-to-get funds on a less-than-vital visit at a time when the department is being forced to cut back.

The widespread nature of that talk inside the State bureaucracy reflects the continued serious strain between the secretary and his small circle of personal advisers, on one side, and members of the Foreign Service on the other. Although career Foreign Service officers traditionally have complained about the political appointees they serve, such grumbling has been particularly acute under Baker and his aides, who are seen as particularly secretive and distrustful, or even disdainful, of the career service.

Two months ago, the U.S. Fish and Wildlife Service announced in the Federal Register that it had just completed a survey on the status of the argali sheep around the world and would shortly consider listing it as a species "threatened throughout its range." Following its review, "the service may classify the entire species or specific populations as threatened or endangered," the Federal Register notice said.

But even the Mongolian government considers the Altai Mountain argali so rare that it allows only 25 to be killed in one year and normally charges hunters, such as Baker, $25,000 for a permit to shoot the animal, according to a spokesman for the World Wildlife Fund. Another subspecies proposed by the Mongolians to Baker, the Gobi Desert argali, is more plentiful; 75 can be taken a year and a permit costs only $13,000, the spokesman said.

The Mongolians originally offered to arrange for Baker and any hunting group he wanted to bring to go after the argali with the Mongolian government paying for the permits.

Baker's reply was that if he came, he and his party would personally pay any fees involved, according to State Department sources.

Tutwiler said yesterday in her statement that Baker told a top Mongolian official three months ago, when the earlier invitation to visit the Altai and Gobi areas where the argali live was discussed, that he would not go unless there was progress toward free and fair elections in that communist country.

When Mongolia's first parliamentary elections since 1921 were scheduled for today, planning was ordered for a Baker trip to that country in conjunction with a meeting of Asian nations in Jakarta, Indonesia.

Critics point out that Baker was flying 4,500 miles out of his way to spend a day in talks with a government that just 10 days ago received its first U.S. ambassador. "It is a two-day hunting trip, primarily," one senior diplomat said, asking not to be quoted by name. "And ask them what it costs to take all those people there," he added.

Tutwiler said Baker would meet with the government leaders and the opposition, as he has in Eastern Europe. Last Wednesday, Mongolian radio reported that the country's prime minister told a news conference that during Baker's visit there will be "talks on trade and economic cooperation, a consular convention will be signed, as well as an agreement on cooperation with the American Peace Corps."

Baker aides conflict more sharply on their stories as to who was responsible for warning him that the argali sheep is a threatened species and possibly an endangered species.

Tutwiler said that Baker, sensitive to hunting such animals, had the department's assistant secretary for oceans and environment, E.U. Curtis Bohlen, research the status of the animals in Mongolia. In addition, another check was made by a personal aide to Baker with the World Wildlife Federation.

Bohlen sent back two memos outlining the situation on wildlife in Mongolia, Tutwiler said. "This is information from our own political appointee at our request," she said.

Other sources said it was a memo from Foreign Service officers who were asked to plan the Mongolian portion of Baker's trip that first noted the threatened status of the argali. They also said the first memo was ignored so they sent another one. This one noted public criticism directed at a Texas political figure who had killed such an animal, and it was that memo which recently caught Baker's attention, these sources said.

Baker's visit to the Atai Mountains was dropped "days ago," Tutwiler said. Instead, he and his wife and their security personnel will go to a recreational area in the South Gobi, about 350 miles south of Ulan Bator, Mongolia's capital. He will pay for his fare and his wife's on the charter flights involved.