The Carter administration, adding to a string of increasingly urgent expressions of concern over Iran, assured the shah of strong U.S. support yesterday and urged him to carry on with the reforms that have provoked snowballing unrest against his rule.

The separate statements from President Carter and State Department spokesman Hodding Carter reflected a growing impression within the U.S. government that Shah Mohammad reza Pahlavi's government is in danger of losing its grip on Iran, vital for its oil and strategic location abutting the Soviet Union and alongside the Persian Gulf.

"It just continues to slide," said one high U.S. officials, describing the situation in Iran since protests broke out in January. "You name it, and it's just been slipping, slipping, slipping . . . The military are now restive. They feel they aren't getting clear enough signals from the shah."

No one development in recent days has led to the sharply increased concern within the administration, officials said, but rather a more clearly defined realization that the momentum of protests and bloodshed over the last 10 months is reaching the boiling-over point.

Presidential security adviser Zbigniew Brzezinski and other high administration foreign policy officials in recent unattributable briefings have been underscoring the dangers that overthrow of the shah would raise.

Carter also emphasized the point yesterday in a statement to the shah's son, Crown Prince Reza, who was visiting at the White House on the occasion of his 18th birthday.

"Our friendship and our alliance with Iran is one of our important bases on which our entire foreign policy depends," Carter told the young prince, who is undergoing training at the U.S. Air Force Academy.

"We're thankful for his move toward democracy," Carter added referring to the shah's liberalization policies. "We know it is opposed by some who don't like democratic principles, but his progressive administration is very valuable, I think, to the entire Western world."

At the State Department meanwhile spokesman Carter said the United States is "remaining in regular contact with senior Iranian officials." but added that the president has not repeated his much-publicized call to the shah during an earlier burst of violence several weeks ago.

"It remains our view that the Iranian government remains capable of meeting the present difficulties, although the violence and strikes pose serious problems to the government's effort to proceed with its programs of liberalization and economic reform," he said. "We believe that these programs are essential and that the government deserves credit for continuing in this direction despite the circumstances."

Opposition by conservative Moslem clergymen to the shah's efforts to modernize Iran and free it from the strictures of traditional Islamic codes is generally believed to have precipitated the popular unrest that has led to hundreds of deaths over the last 10 months.

Added to - and mixed with - the religious friction is resentment of disgrunted middle class Iranians, such as vivil servants, who have been unable to keep up with the inflation brought on by swift oil-financed development.

An Oilfield strike that has sharply cut back exports of crude and natural gas, for example, began as a dispute over pay increases, but has escalated to include broader demands for release of political prisoners and an end to marital law. The army was dispatched yesterday to guard key oil installations against sabotage.

Despite State Department reassurances. U.S. officials clearly are concerned that the spreading unrest could grow beyond the army's ability to keep it in control.

"They (the military) haven't been able to do it on a limited scale so far." said one official. "There's no reason to believe they can do it on a large scale later on."

Washington's preoccupation with the Iranian troubles grows in part from the increasingly important military role the shah has assigned himself in the area and his unservingly pro-Western orientation at the head of a country with a 1,500-mile border with the Soviet Union.

The shah has contracted to buy more than $10 billion worth of American weaponry in the last decade including the most sophisticated warplanes in the U.S. arsenal. His purchases have made him the most powerful ruler in the Persion Gulf area - and would do the same for whoever took over for him if he were overthrown.

Iranian oil also is a major factor in U.S. concern. Ther United States imports about 900,000 barrels of Iranian oil a day, approximately 5 percent on total U.S. daily consumption, and about 10 percent of total U.S. imports of 8.5 million barrels.

The current strike, however, is expected to have little immediate impact on U.S. supplies, because transport from Iran to the United States takes six to eight weeks. Even should the strike drag on beyong that time, officials said, other sources could increase production enought to make up the difference.

"The Department of Engergy is (monitoring) and will continue to monitor the situation" said department spokeswoman Gail Bradshaw. "But there appears at the moment to be no cause for concern."

Also diminishing the prospect of any pinch because of the Iranian strike she added, are crude oil stocks built up in anticipation of a price increase by the Organization of Petroleum Exporting Countries at its December meeting.