NEW DELHI, Dec. 16—Prime Minister Indira Gandhi has written to President Nixon, in a letter released today, that the war between India and Pakistan could have been avoided if the United States had used its “power, influence and authority” to achieve a political solution to the crisis in East Pakistan.

Mrs. Gandhi wrote that despite advice that she gave in August to Henry A. Kissinger; the President's adviser on national security affairs, only “lip service was paid to the need for a political settlement, but not a single worthwhile step was taken to bring it about.”

Mrs. Gandhi said she was writing at a time of deep anguish over the “unhappy turn which relations between India and the United States have taken.” The letter was sent to Mr. Nixon yesterday.

Relations between the two countries, which have been strained because the United States did not denounce Pakistan for her repression of the Bengali movement for autonomy last spring, deteriorated sharply this week with the news that the nuclear‐powered aircraft carrier Enterprise and seven other American Navy ships were heading for the Bay of Bengal.

“India was deeply hurt,” Mrs. Gandhi wrote, “by the innuendoes and insinuations that it was she who had precipitated the crisis and had in any way thwarted the emergence of solutions.”

In what was taken here as an allusion to Mr. Nixon, Mrs. Gandhi continued, “I do not know who is responsible for this calumny.”

She asked President Nixon to “at least let me know where precisely we have gone wrong before your representatives or spokesmen deal with us with such harshness of language.”

Repeating a theme she has sounded several times recently, she said that India did not want to acquire any Pakistani territory for herself in the war.

“We seek nothing for ourselves. We do not want any territory of what was East Pakistan and now constitutes Bangladesh. We do not want territory of West Pakistan.”

She said India wanted only lasting peace with Pakistan. “But will Pakistan give up its ceaseless and yet pointless agitation of the last 24 years over Kashmir?” she asked. “Are they willing to give up their hate campaign and posture of perpetual hostility toward India?”