Leaders of Egypt's Coptic Church said today they still consider Pope Shenouda III their spiritual head despite President Anwar Sadat's announcement yesterday that he was withdrawing state recognition of the patriarch, whom Sadat accused of trying to be too much of a political figure.

The leaders of the Christian sect added, however, that they were not surprised by Sadat's move and that they supported his related crackdown on extremist Moslem groups in a bid to bring a swift halt to the sectarian strife troubling the country.

Insisting that Shenouda, 58, was still "pope of Alexandria and the See of St. Mark," the Coptic leaders said the commission of five prominent bishops created by Sadat to take the pope's place would only handle administrative affairs and relations with the state.

Sadat declared that he was annulling a 1971 government decree "appointing" Pope Shenouda, with whom he has had a running feud for many years, as patriarch of the 5 million Egyptian Copts. Sadat accused him of wanting to become a "political leader" of the Christians and to "achieve certain personal objectives," which he did not name.

A church spokesman said Shenouda was duly elected in 1971 by the Coptic hierarchy and lay representatives in a complicated procedure that involves a drawing by lots. "No one can change it," said Bishop Samuel, head of ecumenical, public and social services for the church.

Bishop Samuel generally had high praise for Sadat's speech, however. Another church source said the hierarchy and Shenouda had been informed about Sadat's decision a week before the announcement. There were indications from what both Sadat and Samuel said that the two sides may have reached a prior agreement.

Samuel described Sadat's crackdown beginning with mass arrests Wednesday night, on the Moslem Brotherhood and other fundamentalist Islamic groups accused of fomenting sectarian strife as a "very courageous act" that "will help the Christians of Egypt and all Egyptians."

More than 1,500 persons, including Moslem and Christian extremists, lawyers, journalists and other political opposition elements, have been arrested in the most sweeping crackdown on religious and political dissent since Sadat came to power 11 years ago.

Samuel attributed the measures taken against the Christians, which also include the arrest of at least eight bishops and priests and the closing of two church publications, as an effort by Sadat to act evenhandedly.

"He has to do this balance," he commented in an interview at his office on the sprawling grounds of St. Mark's Cathedral in central Cairo.

The bishop, a member of the five-member commission set up to handle church-state affairs, had just come from celebrating a mass held in a small 12th century chapel outside the main cathedral. Prayers were said for Pope Shenouda.

The reaction there to Sadat's measures against the patriarch was mixed. One woman was on the verge of tears. Another said she had been told not to talk about it, while a youth said he felt Shenouda was just "so-so" as a pope. None seemed aware that he was still pope so far as the Coptic hierarchy was concerned.

The state-controlled media stressed Sadat's action in ousting the pope and called the commission a "caretaker council" established to replace him. Thus, most Copts are likely to assume Shenouda has indeed been dismissed.

Analysts of church affairs said animosity between Sadat and Shenouda dated back almost to the time of the pope's election in 1971, a year after the Egyptian leader came to power.

A mystic often in retreat to meditate at St. Bishoy Monastry, 60 miles northwest of Cairo, the bushy-bearded patriarch angered Sadat last year by refusing to preside over Easter services to protest Moslem-Christian clashes in Upper Egypt. Shenouda was reported to be at the monastery today, with soldiers posted at the entrance.

Sadat also accused Shenouda of inciting the small Coptic community in the United States to publish an advertisement in The Washington Post during the president's trip to the American capital last year accusing the Moslems of persecuting Christians. The Copts also demonstrated against him during his visit to Washington last month.

In his speech last night, Sadat accused Shenouda of having a "narrow" view of his role and of concentrating too much on the building of churches. While he did not directly accuse Shenouda of instigating Christian extremism, Sadat told the new five-member commission "to end the spirit of hatred and bitterness and bring back to the church the spirit of tolerance, patience and love."

The Coptic Orthodox Church is the largest indigenous Christian one in the Middle East and traces its origins to St. Mark and his founding of the first African church in Alexandria in A.D. 42 It has about 1,200 churches, hundreds of desert monasteries and 1,800 priests in Egypt.