After more than three weeks of escalating student unrest, the martial-law government of President Mohammed Zia ul-Haq today arrested at least a dozen political leaders who have been demanding an end to his 3 1/2 years of military rule, according to reliable reports here.

The crackdown came after the Zia government closed most universities in two provinces and just two days before a meeting of major political figures scheduled for Friday in defiance of martial-law regulations.

In the last three weeks, the Zia government has either jailed or placed under house arrest at least eight other political figures and restricted the movements of three more. Those arrested included three of the nine signers of a Feb. 6 demand for elections within three months. It was issued by leaders of nine political parties who unified under the banner of the Movement for the Restoration of Democracy.

Among those whose movements were restricted are the widow and l daughter of former president Zulfiqar Ali Bhutto, who was executed by the Zia government in April 1979. the widow, Nusrat, and daughter, Benazir, are now leading Bhutto's Pakistan People's Party and Nusrat was one of the signers of the restoration movement's manifesto.

It is difficult to get firm figures on the number of political arrests or the spread of campus violence since the government is releasing little information. There have been no reports in the censored newspapers or on the state-controlled radio. With only a few exceptions, stories of campus unrest have been buried in small notes announcing the closing of universities.

The major source of news of the ferment here has been foreign broadcasts, especially from the British Broadcasting Corp. Word of today's arrests came from politicians calling foeign correspondents here.

A number of political figures were reported to have gone underground today to escape arrest and others said they would try to get to Lahore for Friday's meeting.

Most of today's arrests took place in Lahore, the capital of the Punjab, Pakistan's most populous and politically active province, but a few were reported here in the national capital and its twin city of Rawalpindi.

There was speculation that Zia ordered the mass arrests today because he is leaving Thursday for Saudi Arabia to take part in an Islamic Conference effort to end the Persian Gulf war.

Zia today blamed the student unrest on "local and foreign elements." He insisted that the students do not dislike his government, but are being manipulated by politicians.

After two days of quiet on the campus, meanwhile, violence was reported today at a new spot -- the University of Karachi, where an Army major's jeep was burned while he was investigating a dispute between two student political groups. This was the first time such recent violence had touched Karachi, Pakistan's largest city.

Until now, many observers here have given Zia high marks for handling both the political activity and student unrest. He was described as having acted quickly and firmly, although with restraint, and neither the dissident politicians nor the student demonstrators appeared to have picked up any popular support.

Trade unions, which combined with student demonstrators in 1962 to bring down a previous martial-law government of Ayub Khan, have remained on the sidelines. If they took to the streets, observers here said, the Zia government could be in trouble even though it currently appears firmly in control.

Zia dealt with the student unrest, which started Feb. 9, by closing the schools to disperse the demonstrators. No Army troops have been used, no shots have been fired by police, even when fired on in the Northwest Frontier city of Peshawar, and no students have been killed.

Nonetheless, the student and political ferment comes at a potentially embarrassing time for Zia, who is seeking a more prominent position on the world stage as an Islamic leader trying to end the Iraqi-Iranian war and bring about a Soviet withdrawal from neighboring Afghanistan.

Moreover, his government is quietly wooing the new Reagan administration in the hope that with improved relations, the United States will restore large amounts of economic aid and allow arms sales here. Both were cut as a result of Pakistan's nuclear program that the Carter administration found was designed to produce weapons.

The formation of the Movement for Restoration of Democracy came as a surprise after nine months of public inactivity by politicians. Just forging the nine parties into a common unit was considered a major achievement since ideological and personal grudges between members are common. The Bhutto family originally insisted on a condemnation of the 1977 overthrow of Bhutto, which some political parties had supported.

The signers represent nine of Pakistan's 12 major parties, although it is difficult to say how much popular support any of them have.

Zia had promised to hold elections from the day he seized power, but in October 1979, he canceled voting scheduled for that fall.