A high-ranking U.S. official here said today there is evidence that uprisings that began nine days ago in Hamah, in central Syria, have spread to other parts of the country. The official, who would not let his name be used, would not say what new areas may have been affected, saying the intelligence was fragmentary.

But the official, who has access to sensitive intelligence information, said it was clear that Syrian authorities had provoked the clashes in Hamah, 110 miles north of Damascus, by cracking down hard on dissent. He said Syrian authorities moved in and arrested dissidents, adding that there were unconfirmed reports that some of those people had been shot.

Diplomats here portrayed Syrian President Hafez Assad as a leader in "serious trouble" because of civilian uprisings and opposition within his military.

Besides civil strife, U.S. officials here said Assad is confronted with defections within his officer corps. Jordanian leaders have told U.S. officials traveling with Defense Secretary Caspar W. Weinberger that they were surprised to learn that some of the officers who recently tried to overthrow Assad were from his own Alawite Moslem sect.

"This really surprised the Jordanians," one U.S. official said here tonight.

Coming on top of the reported efforts to unseat Assad is growing evidence that Syrian military officers in some areas are refusing to arrest civilians opposing the president, officials said.

The Syrian government has been insisting, however, to American diplomats here and in Damascus that it has put down uprisings in Hamah with a minimum of force.

Syrian Deputy Foreign Minister Nasser Khaddour summoned U.S. Ambassador Robert Paganelli to the Foreign Ministry at 1:30 a.m. Thursday for what was described as a "stern warning" about a State Department spokesman's comments Wednesday on reports of serious fighting in Hamah, news services reported from Damascus.

Syrian authorities said reports of the revolt in Hamah were slander, but they acknowledged that the city of 100,000 remained sealed off indefinitely. Information Minister Ahmad Iskander told reporters in Damascus that troops in Hamah were pressing a house-to-house search for weapons and hideouts of dissidents. He said, "We have very firm ways of getting rid of criminals," but he gave no details.

He added, "The situation in Syria is very quiet, firm and strong. We addressed to the State Department spokesman an invitation to visit Syria as a tourist to see for himself." Asked by reporters if they could go to Hamah in the spokesman's place, Iskander said "possibly," after the "criminals have been arrested."

Western diplomatic and other foreign sources in Damascus said that fighting continued Thursday between rebel Sunni Moslems and approximately 8,000 Syrian troops shelling Hamah for the ninth day. Casualty figures could not be estimated accurately, but diplomatic and other accounts said the number of killed is in the hundreds and damage extensive, The Associated Press reported.

The clashes in Hamah followed reports of a recent coup attempt, which did not appear directly related to the current fighting, and a series of bomb blasts in Damascus late last year for which the outlawed opposition Moslem Brotherhood was blamed.

Hamah is populated by Sunni Moslems and has long been considered a center for activity against the regime dominated by Assad's minority Alawites, 11 percent of Syria's population of 9 million.

Weinberger is in Jordan to discuss this country's need for arms and the overall military situation in the Middle East and has not dwelled on the strife in Syria, officials said. This may change, however, if the situation in Syria worsens, they said.

Weinberger and King Hussein met today to discuss weapons Jordan wants for protection against air attack. Hussein has ordered mobile antiaircraft missiles from Moscow, a step Weinberger had hoped to reverse.

Hussein told reporters today that he intends to go through with ordering SA8 antiaircraft missiles from the Soviet Union. "This has been concluded some time ago and I don't think it will change," he said. The missiles "will be delivered."

Under that arrangement Iraq will pay $200 million for the Soviet missiles. U.S. officials admit that they cannot match the low price the Soviets have set on their mobile missiles, but they say they still have hopes that Hussein will turn to the United States for much of his future weaponry.

U.S. officials said tonight that Hussein expressed interest in buying mobile versions of the improved Hawk antiaircraft missiles. The Hawk missile-launchers now deployed by Jordan are bolted to concrete pads, making them an easy target for modern aircraft.

Weinberger and Hussein also discussed the possibility of Jordan buying the General Dynamics F16 fighter, officials said. Hussein told reporters that he had not been offered the plane, but a defense executive here said, "The ball is in the king's court."

Hussein has not yet indicated whether he wants to buy the F16 or the Northrop F5G fighter, the official said.