Prime Minister Indira Gandhi told a gathering of 2,500 Indians yesterday that she had mixed feelings about their emigration from India to the United States and appealed for their help in India's development.

Winding up her four-day visit to Washington during which she met President Reagan and other administration officials, Gandhi was given a standing ovation by her Kennedy Center Concert Hall audience of Indian families who are among the area's estimated 22,000 Indians.

Attired in a plain turquoise sari, the 64-year-old Gandhi, accompanied by her son and heir apparent, Rajiv, displayed both warmth and steeliness as she tiptoed through controversial topics.

"I was asked yesterday whether I resented Indians coming away from India ," she recalled. "I said my reaction is a mixed one.

"We would naturally like them to remain and help their own people and serve our country," said Gandhi who heads a country of 700 millionpeople, which like most developing nations has problems in keeping its skilled and professional people from seeking greener economic pastures abroad.

"At the same time we feel we are part of a larger humankind and if Indians can help human progress . . . then that is a worthwhile job and we should be glad that they do this," she added.

"We look to Indians here to see in what way they can help out, perhaps by investing to start new industries or by giving their time and advice, not necessarily leaving their jobs here, and coming for a short while to India."

Kamal K. Mittal of Gaithersburg said Gandhi's speech, which she delivered mostly in English, switching briefly to Hindi at the end, was "super" and expressed the hope that her visit to the United States, the first in about a decade, would ease the "stressful" relations between the two countries that "did not reflect what the people felt for each other."

Mittal, a medical researcher at the National Institutes of Health, is an Indian who came to the United States in the last decade under immigration regulations that help make entry easier for professional and skilled people.

The majority of the Washington area's Indian community are immigrants who are still Indian citizens, said James Rao, a medical lab technician who helped coordinate the 27 Indian organizations in this area that jointly sponsored yesterday's meeting. A smaller group that Rao estimated at 6,000 to 7,000 is composed of naturalized U.S. citizens, and a third group comprises about 3,000 Indian university students. Most of the Indian community is concentrated in Montgomery County, Rao said.

The meeting opened with the singing of the Indian and U.S. national anthems. Many women in the audience, like Vijay Kumari and Lalita Erry of Arlington, were dressed in saris. And many expressed warm feelings for "Shrimati" or Madam Gandhi.

"To see Mrs. Gandhi is only once in a lifetime," Rao said. "We do not know if she will be reelected as prime minister. She is a very outspoken lady even though she is a mother and has a family. She explains things as she sees them."

"It is for the people to be in touch with their roots no matter how far they travel or how high they climb and to work for better relations between the two countries, which is as much to your advantage as to us in India," Gandhi told the group. "So we expect Indians who are here to do their jobs well and bring credit to our community, but also to build bridges of friendship and cooperation between East and West."