President Carter kept a restraining hand on the American military yesterday at the same time his spokesman took a more strident line in denouncing Iran's treatment of American hostages in Tehran.

Although the aircraft carrier Kitty Hawk and her armed escorts continued to steam from the Pacific toward the Indian Ocean, few other military actions were ordered in reponse to what officials fear is a deteriorating situation.

Pentagon spokesman Thomas B. Ross said no alert has been issued to any American ground force anywhere in the world, despite rumors to the contrary flying around Washington last night.

Navy sources doubted the Iranian navy could mind the straits of the gulf even it chose to do so. Iran is short on ships and gear for laying mines. In addition, Iran's navy, as well as the rest of its military, is lying low during the current political turmoil in Tehran.

For Fear Iran might try to mine the straits eventually despite those difficulties, the Navy yesterday sent helicopters for laying or clearing mines from the East Coast to its Pacific fleet aboard Air Force C5 transports.

The ships that Iran could deploy to protect a mine-laying operation in the gulf would be no match for U.S. firepower in the area, military officers said.

Iran has two American destroyers of about 3,000 tons, some smaller British warships and several speedy patrol boats. But the Iranian air force, decimated mechanically by lack of spare parts and spiritually by the execution of military leaders, including former Air Force commander Hossein Rabii, could not protect those ships from U.S. fighter-bombers.

The U.S. aircraft carrier Midway, already in the Arabian Sea near the entrance to the Persian Gulf, is armed with about 60 warplanes, including Al, Am and F4 fighter-bombers which could attack Iranian ships. The Midway also carries a few tanker planes for refueling fighters in midair to extend their range.

Protecting the Midway, and adding to the firepower available for any fight in the Perisan Gulf, are the nuclear-powered cruiser Bainbridge, the destroyer Parson, and the frigates Knox and Stein.

The Kitty Hawk, once it reaches the Persian Gulf area in about a week's sailing time, will more than double the airpower that could be used against southern Iran, where the oil fields are located. The Kitty Hawk carries about 87 planes, most of them fighter-bombers.

Sailing along with the Kitty Hawk are the guided missile cruiser Jouett, guided missile destroyer Berkeley, destroyer David R. Ray and frigate Fanning.

If President Carter should end up ordering the plans from those carriers to attack Iran, the naval task forces most likely would steam right up the Persian Gulf to increase the bombers' striking range.

Because Tehran is about 400 miles north of the gulf, fighter-bombers would have to be refueled enroute to make the flight from the carrier to Tehran and back. This would be a difficult operation.

From a strictly military standpoint, but not a political one, the oil fields at the head of the gulf around Agha Jari would be much easier to hit.

Troop-carrying helicopters have an even shorter range than fighter-bombers, virtually putting Tehran out of reach from carriers in the Persian Gulf. One battle-experienced general said the United States would have to seize an airfield near Tehran and land armor and troops there before mounting any successful ground assault against the Iranian capital.He estimated a division of 20,000 troops would be required.

The United States also has two aircraft carriers in the Mediterranean, the Independence and the Nimitz. But here again the long distance to Iran makes strikes from the Mediterrranean unlikely.