The Moslem group linked by Western diplomats here to the assassination of president Anwar Sadat represents the most radical edge of a deeply rooted, extremist religious movement that for generations has been combating secularlism and Western influence in Egypt and throughout the Middle East.

The Takfir wa Hijra (Repentant and Holy Flight) organization first became known in Egypt in the early 1970s, at a time when Sadat's relative tolerance of political activism encouraged the spread of conservative religious groups and his growing ties to the West angered extremists who believed the nation should be ruled by the strictures of Islamic law.

The Takfir was a spinoff group from the clandestine Islamic Liberation Party, which operates in many Arab countries and in Egypt was charged with an attempted coup in 1974 after an attack on the Egyptian Military Technical College. Like similar political and religious drives in other Arab nations, the Takfir proclaimed its rejection of all modern, Western innovations -- as well as the more tolerant form of Islam that Sadat adhered to -- as an "infidel system."

The Takfir is said to be associated with Sadat's assassination by Western diplomats here in contact with Egyptian authorities. It has not yet been blamed for the killing by the government, nor has it claimed responsibility for it. Moreover, diplomats were not sure today to what extent the assassination squad was organized by the Takfir, or how deeply the group's support extends into the ranks of the military.

Nevertheless, the Egyptian defense minister, Lt. Gen. Abdel Hamlin Abu Ghazala, and other officials made clear they believe Sadat's murder was inspired by the kind of Islamic extremism found in the Takfir and its counterparts in Egypt and throughout the Arab world.

From the mountain redoubts of Afghan rebels and chaotic urban streets of Iran to the puritannical institutions of Saudi Arabia and tense mosques of Tunisia, this kind of Islamic movement has become a political as well as religious drive with consequences rivaling those of the Christian crusades 900 years ago.

The traveler notices the signs. The number of veiled women in Cairo is on the increase, casting a shadow over this city's reputation for tolerance. European airline offices in sparkling new Saudi shopping centers lock their doors for sunset prayers so employes can chant, "God is great, god is great."

Even easy-going Filipino women on pilgrimage drape white robes from head to toe for the journey to Mecca, which climaxed today with an estimated 2 million Moslems crowding around Mt. Arafat for observances of the Id Al Adha holiday.

Beneath these symbols, deep currents are flowing, creating instability in a number countries and presenting the United States and its Western allies with a new and unfamiliar challenge.

The most obvious of these is in Iran, where an old Islamic preacher became the patriarch of a revolution still running its course. Ayatollah Ruhollah Khomeini's voice has been heard around the world, and his message is so startling that many in the West have had trouble believing it. Yet, the Koranic scholars have from the start told Iranians they were right to resent the Western onslaught on their traditional values.

The force of this argument, even outside Iran, was demonstrated during the November 1979 takeover of the Great Mosque at Mecca, Saudi Arabia. An Iranian radio broadcast blaming the United States for the sacrilege led to the sacking of the U.S. Embassy in Islamabad, Pakistan, and, at about the same time, helped along an attack on the U.S. Embassy in Tripoli, Libya.

Almost coinciding with the Mecca Mosque takeover was an uprising by Shiite Moslems -- members of the same sect as Khomeini's -- in an eastern province of Saudi Arabia. Although the trouble was not directly linked to the Iranian revolution, diplomats and other observers in Saudi Arabia believe the Islamic surge fostered by Khomeini and his followers contributed greatly to the violence.

The Mecca attack itself, although the plotter's motives remain sketchy, reflected Islamic reaction to the Saudi's royal family's drive to modernize its kingdom by force-feeding the 20th century into what until recently had been an isolated desert people defined mostly by tribes.

It was Egypt -- seat of Islam's prestigious Al Azhar University -- that produced some of the earliest signs of modern Islamic reaction against the West. An Egyptian teacher named Hassan Banna founded the Moslem Brotherhood here half a century ago, demanding strict adherence to Islamic law in a country already heavily influenced by European ways.

Sadat himself once was associated with the Moslem Brotherhood, attempting to use its resentment against the West as a tool to fight British occupation during the early days of the Free Officers' Movement, which eventually brought Gamal Abdul Nasser to power in 1952.

But Sadat more accurately reflected the tolerant brand of Islam that traditionally had been practiced in Egypt. Although often seen at prayer on Friday in Mosques around the country, he also opened Egypt to Western influences and goods and sought to model his economy along Western lines.

Perhaps more importantly, Sadat inherited from Nasser an Egypt whose mission as leader of Arab nationalism already was compromised by defeat in the 1967 war with Israel, and he went on to push it toward peace with the Israeli enemy -- upsetting an animosity that had been a national rallying point for a generation. Robbed of their pan-Arab role and told that "Zionist enemies" were now to become Israeli tourists, many Egyptians turned to Islam in reaction to the swift pace of change.

Members of the Tafkir were among the 1,500 arrested last month in Sadat's crackdown on the religious groups. Its adherents have been arrested since 1975 and were the focus of a major government campaign in 1977 after the kidnaping and murder of a former minister of religious affairs.