Prime Minister Rajiv Gandhi, charging that his mother was the victim of a foreign-linked conspiracy, said today that Indira Gandhi's assassination should be avenged, not in anger but through efforts to unify a strong and modern India.

In his first appearance at a public rally since being sworn in as prime minister on Oct. 31, Gandhi said the assassination was "not to remove just one person, but to shatter the stability of the country."

Returning to the same theme twice more in a 12-minute speech at a gathering to commemorate Indira Gandhi's 67th birthday, the prime minister said:

"We are seeing that there was a conspiracy behind Mrs. Gandhi's assassination and there were certain elements active in foreign countries . . . We have to find the origins of this conspiracy. We'll have to see from where they are getting their support."

He offered no specifics on the source of the conspiracy but said that the expectations of those who had wished the Indian union to unravel in the aftermath of the assassination had been proved wrong.

While the Indian press has presented a flurry of mostly speculative conspiracy stories since the assassination, no government offficial has publicly offered specifics beyond general insinuations that Sikh separatists living abroad were involved. Gandhi was shot to death in the garden of her home by two Sikh security guards.

"We must avenge her death," Gandhi said, and before he could continue the sentence a ripple of applause quickly grew into the most vociferous expression of approval by the outdoor crowd of approximately 200,000 supporters. Gandhi hastened to add, "not in anger, but by working hard to keep the country together."

Alluding to the anti-Sikh riots following the assassination that left at least 1,500 persons dead, Gandhi said, "When a large tree falls, the earth shakes. But the world can see and is seeing that India is independent and strong. We must see that the work of Jawaharlal Nehru and Indira Gandhi is completed." Nehru was Indira Gandhi's father and India's first prime minister.

Repeatedly during what, in effect, was his first campaign rally, Gandhi invoked the memories not only of Nehru and his mother, but also that of Mohandas K. Gandhi, the apostle of nonviolence who led the independence movement but who was no relation.

"When a person rises to her Indira Gandhi's stature, she doesn't leave us, like Mahatma Gandhi, who was shot 36 years ago and whose ideals are still alive and he is still alive. Similarly, she hasn't died in the hail of bullets," he said.

Speaking at a podium atop a 15-foot-high platform on the broad mall that runs alongside New Delhi's imposing Raj Path, Gandhi was flanked by two oversized and flower-garlanded portraits of his mother and banners quoting from her speeches. One read: "Whatever religion we are, wherever we come from, we are all Indians."

Another banner declared, in Hindi, "The nation's mother, Indira Gandhi, lives forever." Ostensibly, the rally was a "public meeting" to commemorate Indira Gandhi's birthday, but its organization and tenor had undertones of an election campaign rally of supporters of Gandhi's ruling Congress (I) Party.

More than 600 buses and trucks were requisitioned by the city administration to transport party supporters from outlying areas, and Congress (I) flags and banners were prominent in the crowd that stretched as far as the eye could see, from the Parliament building nearly to the imposing pink sandstone Gate of India arch half a mile away.

The crowd waited for more than two hours as the All-India Radio choir sang laments in memory of the slain prime minister, including one whose Hindi lyrics translate, "Indira Gandhi, the mother, your words have become immortal. You were the hope of Gandhiji Mahatma Gandhi and the daughter of Jawaharlal Nehru. You are the epitome of Durga, the goddess of victory."

H. K. L. Bhagat, the minister of information and broadcasting, admonished the crowd not to shout any slogans other than, "Indira Gandhi amar rahe" ("Indira Gandhi lives forever"). But immediately after Gandhi finished his speech, Bhagat went to the microphone and began to lead the chant, "Rajiv Gandhi zindabad" ("Long live Rajiv Gandhi"). The new prime minister abruptly diverted him from the microphone.

Security was tight for Gandhi's first appearance before a large crowd since his mother's assassination. Hundreds of paramilitary police and border security forces ringed the podium, and sharpshooters were positioned atop nearby buildings and even hidden amid the foliage of a large tree directly in front of the podium.