The Pakistan army, promising fresh elections in October, put the country under martial law today after taking control of the government and arresting Prime Minister Zulfiqar Ali Bhutto, Radio Pakistan said.

In a radio address to the nation, army chief of staff Gen. Ziaul Haq said President Fazal Elahi Chaudhry would continue as head of state. He said the country will be administered, by a four-man military council.

Gen. Ziaul, 52, said he had taken over as chief martial law administrator to assure "free and just elections which God willing, will be held in October."

He announced dissolution of the National Assembly and state assemblies and removal from office of all Cabinet ministers and state governors.

The 1973 constitution is to remain in force "although some provisions . . . will not be in effect," he said. All political activity has been suspended but the ban will be lifted in time for the October vote, he added. No details of the proposed election were disclosed, including whether Bhutto or other figures arrested by the army can take part.

In the interim, Pakistan's four provincess will be governed by the chief justices of the provincial supreme courts.

The early morning coup appeared to have been accomplished without bloodshed and the nation appeared to be calm. Indian sources said that air and rail links were functioning normally.

The military takeover followed four months of political unrest over opposition charges that Bhutto had rigged the March national election in which his party scored an overwhelming victory. Hopes that a negotiated solution, involving fresh elections, faded late last week when the two sides began accusing each other of bad faith.

In his broadcast, Gen. Ziaul said the army had refrained from intervening before because it hoped a political solution could be found. He dismissed what he said were suggestions that the coup had been "secretly concented" with Bhutto.

Such an air of distrust has been created during the past few months that even well-meaning people also get bogged down in doubts and apprehensions," he said.

"I genuinely fell that the survival of this country lies in democracy and democracy alone."

"I want to make it absolutely clear that neither do I have any political ambitions nor does the army want to be distrated from its profession of soldiering," added the general, who was appointed army chief of staff by Bhutto in March 1976.

He promised that he would not deviate from a schedule aimed at transfering power to elected representatives soon after the new elections.

Ziaul warned, however, that "if any citizen distrubs law and order in the country, he will also be severely dealt with."

He said that Bhutto and senior leaders of the prime minister's Pakistan People's Party as well as leaders of the opposition group, the Pakistan National Alliance, had been put under "temporary protective custody." One exception, he said, was Begun Nasim Wali Khan, wife of Khan Wali Khan, leader of the banned National Awami Party who is now on trial for plotting against the state.

An opposition newspaper, Nawa e Waqt, reported that Bhutto had been taken to Muree, a hill resort about 35 miles north of Islamabad.

Gen. Ziaul said the military government would honor all agreements with foreign countries negotiated by the Bhutto government.

[In Washington, State Department spokesman John Trattner said that the coup was "an internal matter on which we will not have any comment."]

In neighboring India, which has fought three wars with Pakistan, Defense Minister Jagivan Ram said, "What has happened is an internal affair of Pakistan but some internal matters of a neigboring country have their repercussions on us."

Ziaul is described by associates as a dedicated soldier with no personal political ambitions. A devout Moslem he made a pilgrimage to Mecca earlier this year.

He is said to be a strict discplinarian who nonethless is highly respected by his men. Stockily built and about 5-foot-6, he has a drooping moustache and a reputation as a meticulous dresser.

He was born in East Punjab, which now forms part of India. In 1945, two years before Britain gave Pakistan and India their independence, he was given a commission in the Guides Cavalry at the Royal Indian Military Academy at Dehru Dun. During World War II, he saw combat in Burma, Malaya and Indonesia.

Ziaul was graduated from command and staff college in 1955. He also attended an advanced armored school and the Command and General Staff School in the United States, in 1959 and 1963 respectively.

He served in the Pakistan-India wars of 1965 and 1971.