The military ouster of Prime Minister Zulfiqar Ali Bhutto this week has come as a relief to many Pakistanis, exhausted and dispirited by three months of blood-letting, destruction and political battling.

A considerable number seem skeptical, however, that Gen. Zia-up-Haq, the army chief of staff who seized control of the government Tuesday, will keep his word and hold new general elections in October.

"I believe General Zia when he says that he has no political interests," said a middle-ranking civil servant in the major industial center Karachi. "But power is intoxicating. Have you ever heard of a military dictator willingly giving up power?"

Zia, who arrested Bhutto and about 40 other leaders from the government and the opposition parties, without violence, has promised to hold elections within 90 days. This schedule had been tentatively agreed on by Bhutto and the opposition Pakistan National Alliance.

The alliance had claimed that Bhutto missively rigged the elections last March. This contention plunged Pakistan into an orgy of politically motivated rioting and killing that eventually produced the coup.

The basic that Pakistanis have welcomed the takeover, so far, is that it has halted the violence, which caused at least 350 deaths and cost the nation's economy more than $1 billion.

Because the takeover has been greeted with a sense of relief, the army has kept an extraordinarily low profile. A handful of armed troops are on duty at airports, telecommunications offices and a few other strategic locations. Otherwise, life is normal. No curfews have been imposed.

Newspaper are gradually beginning to comment on the army's move. In a typical editorial, the English-language Dawn, of Karachi, said, "A tranquil mood already seems to have descended upon the country. The armed forces have stepped in only to provide the country with an interim administration."

Most doubts existing in the minds of Pakistanis are based on their repeated experiences with military dictators since the birth of Pakistan in 1947. Democracy has been the exception during the nation's erratic 30-year independent history.

But Zia himself is a highly respected officer who, well before he seized power, frequently told soldiers being involved in politics.

"I know him well," a foreign diplomat in Islamabad said, and "he knows that the days when a strongman could stay in power indefinitely are gone in Pakistan. He knows the people won't stand for it and will fight the army in the streets."

It was just such a situation, with the army battling unarmed civilians to keep Bhutto in office, and the prospect of this kind of violence flaring again, which drov Zia to remove the flamboyant premier.

Explaining his move in a nationwide broadcast Tuesday night, Zia said he believed that Bhutto's Pakistan People's Party and the nine-party Pakistan National Alliance were incapable of reaching a compromise. This failure to agree, he said, "would throw the country into chaos and the country would thus be plunged into a more serious crisis. THis risk could not be taken. The army had, therefore, to act."

In what has been his only public statement since coming to power and imposing martial law, the general said that the post-election violence had assumed such proportions "that people even started saying that democracy was not workable in Pakistan."

But, he added "I genuinely feel that the survival of this country lies in democracy and democracy alone."

Although he maintained an even-handed approach in his broadcast, ascribing neighter blame nor praise to either side, Zia credited Bhutto's opponents with producing a flowering of Islamic values.

"I must say that the spirit of Islam demonstrated during the recent movement was commendable," he said. "It proves that Pakistan, which was created in the name of Islam, will continue to survive only if it sticks to Islam."

Zia's own deep faith as a Moslem has contributed a great deal to the positive acceptance of his takeover. He fulfills the obligatory five sessions of prayer every day, has made pilgrimage to Mecca, and has abolished drinking in regimental messes, halting a rockbound tradition of the Pakistan officier class.

A diplomatic observer noted that those leaders of the opposition Alliance who have not been arrested are those affiliated with the group's extremely conservative religious-based parties.

One of these leaders, Mian Tufail Mohammed, head of the Jamaat-Islami Party, was the first leading political figure to publicly applaud the imposition of martial law, Tufail is a relative of Zia's.

Some observers are beginning to conclude that Zia will use the preiod before he allows political activity to resume to press for Islamic-style government. But in 1970, during nationwide elections which ultimately caused the secession of East Pakistan (now Bangladesh), all religious parties throughout the country received only 12 per cent of the vote.

"Pakistanis like to think of themselves as deeply Islamic," a Western diplomat said, "And they are. But they still perfer to have secular leadership in government."

Meanwhile, Bhutto, his chief opponent, retired Air Marshal Asghar Khan, and other political leaders who are confirmed in government rest houses near the mountain rsort town of Murree, are expected to remain in custody for another two to three weeks.