The Indian government ordered elections today for Sept. 22 in the predominantly Sikh state of Punjab, acting less than a month after signing an agreement with moderate Sikhs aimed at ending three years of sectarian conflict.

Some mainstream Sikh leaders have questioned the viability of early elections, and extremists have threatened new violence.

Harchand Singh Longowal, who signed the agreement in July on behalf of the main Sikh political party, Akali Dal, said earlier this week that "the situation is not ripe" for elections in Punjab. He sought voting in February, after the Punjab agreement was consolidated.

Many Indian political analysts and most opposition leaders have echoed Longowal's worries that an early campaign would revive tensions eased by the accord.

More than 2,000 persons have been killed in the Punjab since Sikh unrest turned violent in 1982, and the state is under direct rule by the central government. But New Delhi's authority to administer the state runs out Oct. 6, and the government chose to hold elections there rather than seek a constitutional amendment necessary to prolong its control.

By calling the elections -- for a state assembly and for representatives to Parliament -- Prime Minister Rajiv Gandhi will pit his own Congress (I) Party against his partner in the Punjab settlement, Longowal's Akali Dal.

"The two sides will attack each other intensively in an election campaign and will reopen the Punjab's wounds," said Kuldip Nayar, a syndicated columnist.

Sikh extremists, who oppose the agreement between the government and the Akali Dal, have vowed to use violence to prevent its implementation. Indian commentators and politicians, including the leaders of most of the opposition parties, worry that the extremists could use elections to encourage renewed fighting between Sikhs and Hindus.

Tensions and mistrust between the two religious groups have been especially high since June 1984, when the government sent the Army into the Sikhs' most sacred shrine, the Golden Temple in the Punjab city of Amritsar, to battle armed Sikh extremists. At the end of October, prime minister Indira Gandhi was assassinated, apparently by Sikh bodyguards, setting off riots by Hindus against Sikhs.

Since Rajiv Gandhi succeeded his mother, he has been trying to defuse the Sikh-Hindu tension. Last spring he released Longowal and others from jail and opened negotiations on their demands for increased political power and economic concessions in the Pnjab.