The Arabs of Khuzestan Province, the center of Iran's oil industry, were reported today to be demanding new political concessions and more money underscoring this country's simmering problem with national minorities.

Their demands represent a far greater challenge to the feeble central government authority than similar demands expreviously other by other minorities because Khuzestan's oil provides Iran with its only major foreign exchange earnings.

Newspaper reports here said 10,000 Arabs demonstrated peacefully yesterday in the oil center of Ahwaz in southern Iran.

They demanded a larger share of oil revenues for Khuzestan, representation in the central Cabinet, priorities for Arabs in Khuzestan's provincial jobs, and use of Arabic as the province's first official language instead of Persian.

Also symptomatic of the revolutionary government's minorities problem were reports that the Turkoman minority staged a general strike today in its unofficial capital of Gonbad-e-Kavus near the Caspian Sea in northeastern Iran.

The strike stemmed from disturbances yesterday in the Caspian port of Bandar-e-Shah between its predominantly Sunni Moslem Turkoman population and the Shiite Moslem minority of Persian speakers who wanted to change the town's name to Bandar-e-Islam. About 90 percent of Iran's 35 million inhabitants are Shiite Moslems and Shiite leaders have been at the forefront of the revolution against the shah.

Spokesmen for the half million Turkomans said they wanted the Turkoman language taught in schools, more central government investments and their own province with their own governor general. At present, the Turkoman population is divided between two predominantly Persian provinces.

Since the triumph of the revolution a month ago and the collapse of an effective army, one national minority after another has taken advantage of the central government's weakness to demand varying degrees of local autonomy.

Lying on the margins of Iran's Persian-speaking heartland, the minorities share membership in Sunni Islam, the majority sect throughout the Islamic world with the exception of Iran and possibly Iraq, where they are outnumbered by Shiites.

Leading the movement were the Kurds in western Iran, the most politically experienced minority whose fellow Kurds live in Iraq, Turkey, Syria and the Soviet Union. Iranian Kurds, who were involved in the short-lived autonomous republic in 1946 that collapsed despite initial Soviet aid, are in affective control of most of Kurdistan.

Next in line were the Baluchis of southwestern Iran whose more numerous Pakistani cousins long have been a thorn in their central government's side, and at times have threatened independence.

Khuzestan itself originally was an Arab province. But after the discovery of oil in the first decade of the 20th century, Iranians from all over the country flocked in.

Iranian census statistics have been notoriously inaccurate concerning the breakdown of Arab and non-Arab residents of the province. Until Iran and Iraq settled their long political dispute in 1975, the Baghdad government claimed Arabestan -- as it called Khuzestan.

So far Ayatollah Ruhollah Khomeini and the provisional government of Prime Minister Mehdi Bazargan have sought to placate the minorities by granting some, but not all, of their demands.

But federation in one form or another, favored by many minorities, is not included in the new draft constitution, according to its drafters.

Observers are convinced that inevitably the Tehran government will be tempted to reassert its traditionally strong central authority throughout the country. But for the president, Tehran can do little more than temporize because of the armed forces' disarray.

Significantly, the country's largest minority, the Turkic-speaking Azerbaijanis of northwestern Iran, have yet to make formal autonomy demands, although for more than half a century they, too, underwent the monarchy's stern efforts to make all Iranians speak Persian.

Various theories are advanced for the Azerbaijanis' relative lack of zeal.

They range from the Shiite faith shared with the Persians to bitter memories of the post-World War II autonomous republic that was crushed mercilessly after the Soviets withdrew their support. The Azerbaijanis are well aware tht they share a common border with the Soviets, and that the Kremlin for more than a century has occupied territory inhabited by other Azerbaijanis.

Meanwhile, revolutionary tribunals ordered the executions of five more Iranians -- identiied as three former officials, a rapist and a man who had forced his wife into prostitution.

Since the executions began last month 30 Iranians have been reported killed for offense under the shah's regime and 16 for sexual deviancy of one form or another. Justice Minister Assadollah Mobasheri confirmed reports that a large but unspecified number of judges, including those on the Supreme Court, would be retired, and that the Justice Ministry and court system would be reformed.