The anti-government revolt in the city of Hamah is being put down at the price of heavy casualties, and, even after the rebellion is totally quelled, extremist sedition could continue to hamper President Hafez Assad's rule, Western diplomatic sources say.

Syrian troops are using artillery and tanks to end the largest challenge so far to President Hafez Assad's rule. The two weeks of clashes in Hamah capped nearly three years of antigovernment agitation blamed on Moslem Brotherhood terrorists.

Casualties from the revolt are estimated by Syrian and diplomatic sources to reach into the hundreds. Destruction is reported considerable inside the still-closed city, 120 miles north of Damascus.

The antigovernment campaign began with assassinations in the spring of 1979. Despite a tough response by Assad and his military establishment, it has persisted and risks becoming an obstacle to Syrian efforts to rally Arab support around Damascus as the front line against Israel.

Syrian officials insist that the 220,000-man armed forces, the key to Assad's strength as president, have remained staunchly supportive of the government. Their assertions are backed up by the judgment of diplomats stationed here, who say no evidence has surfaced to suggest Assad's 12-year-old government is in immediate danger.

"He is firmly in control," said a European diplomat with two years' experience in monitoring Assad's government.

At the same time, terrorism has been a constant source of embarrassment and distraction in Assad's struggle to deal with foreign policy problems afflicting his strongly anti-Israeli government, particularly during the past two months as he sought to fight back against Israel's annexation of the Golan Heights.

As Assad tried to gather increased Arab backing in the heat generated by Israel's Dec. 14 decision to annex the Golan Heights, security has been further tightened, particulary in the capital, which already looks like an armed camp.

Recently, trucks have been banned from streets around Assad's residence, foreign residents of the neighborhood report, since his soldiers flagged down a six-wheel truck loaded with explosives in crowded Omayyad Square, near Assad's residence and that of Foreign Minister Abdul Halim Khaddam.

On Nov. 29 a bomb-laden panel truck exploded in downtown Damascus, killing about 200 persons.

In addition, the Hamah revolt has been raging as Khaddam tried unsuccessfully to persuade Arab foreign ministers at a special Tunis meeting last week to cut off economic relations with Israel's Western supporters, chief among them the United States.

Against this background, the official Syrian media have linked the uprising to Syria's effort at the United Nations to get mandatory Security Council sanctions against Israel and, failing that, isolation of the Jewish state and its allies.

Defense Minister Mustafa Tlas, for example, told the Syrian Cabinet yesterday that discovery of U.S.-made weapons in Hamah's rebel strongholds proved the revolt's "close connection with American imperialism and Zionism," according to a version of his remarks broadcast by the official Syrian radio.

Syrian suspicions also were hightened by a statement from the State Department spokesman last week confirming reports of the trouble in Hamah. The report led to a formal protest by Khaddam to U.S. Ambassador Robert Paganelli.

"By taking the initiative in releasing fabricated reports about the internal situation in Syria, the United States thought it was avenging its big defeat inflicted by Syria at the United Nations," wrote Al Baath, the official newspaper of Syria's ruling Arab Baath socialist party.

The antigovernment exiles claimed the Hamah revolt was matched by simultaneous uprisings in Aleppo and Latikia. The exiles appeared to be trying to suggest broad popular support for the Hamah rebels. Syrian and diplomatic sources agree, however, that the violence was confined to Hamah, despite earlier troubles in the other cities.

Hamah has long been a flash point for Islamic fundamentalism. Women who drive daily in Damascus fear to take the wheel there. Shops that sell alcoholic drinks have been targets of bombings. Veils are standard dress for female pedestrians, even though they are rarely seen in the capital and most other Syrian cities.

At least three times in the past two decades has the Syrian Army intervened to put down Islamic insurgents in the city of 300,000. Diplomatic sources said troops had pulled out only last fall after a months-long occupation imposed because of similar, although smaller-scale trouble last year.

The extremist Moslem Brotherhood, strong in Hamah, is a natural enemy of Assad's government.

The Baath Party government, although it accepts Islam as a source of jurisprudence, is founded on secular principles similar to Western socialism, to stimulate a renaissance in the Arab world. Baath means renaissance in Arabic.

Since an assassination attempt on Assad 18 months ago, brotherhood membership is punishable by death.

In addition, Assad's government has relied extensively on members of his own Alawite sect to fill key positions, particularly in the armed forces. The hardest fighting in Hamah, for example, was carried out by troops from the Army's Defense Brigades, commanded by Assad's brother, Rifaat, with help from a presidential nephew, Adnan Assad.

The Alawites, a 12 percent minority of Syria's 10.5 million inhabitants, are viewed as heretics by conservative Moslems from Syria's 70 percent Sunni majority--expecially fundamentalists such as those attracted to the brotherhood. The little known sect, centered in northwestern Syrian farmland, is an offshoot of Shiite Islam, which differs with Sunnite Islam mainly over the line of legitimacy descending from the Prophet Mohammed.

The religious opposition also has been encouraged by economic and political dissatisfaction even among tolerant Sunnis, who form the vast majority of the population, diplomatic sources say. The relative importance of political as against religious opposition is difficult to judge accurately, they add, but each is thought to nourish the other.

Moreover, Syria is surrounded by unfriendly neighbors who, the informants say, could encourage supplies for the Moslem Brotherhood terrorists, as maintained by the Syrian government.

Jordan, accused by Syria of harboring brotherhood training camps, has become closely allied with Iraq, a traditional Baathist rival of Syria. Iraq's rulers long have been blamed for sedition in Syria because of Baathist doctrinal differences and a heritage of mutual troublemaking, said to include personal animosity between Assad and the Iraqi president, Saddam Hussein. In addition, Saddam Hussein has accused Syria of siding with Iran in the Iranian-Iraqi war and antigovernment Iraqi agitators are known to find refuge in Damascus.

In Lebanon, Maronite Christian militias who originally engineered Syria's entry into Lebanon in 1976 have vowed to expel the 22,000 Syrian troops stationed there, accusing Assad of wanting to absorb the troubled little country. And Israel, which has helped the Maronite leadership, has a strong interest of its own in weakening the Damascus government.

"In this situation, it is difficult to know who could be exploiting whom," a diplomat said.