WASHINGTON, Nov. 29— President Nixon has sent personal messages to India, Pakistan and the Soviet Union urging an end to the fighting along the India‐Pakistan border, the State Department announced today.

The messages to India and Pakistan, a reliable source reported, called for a military de-escalation and withdrawal of forces from border areas.

The note to Moscow reportedly asked the Soviet Government to continue to use its influence with India, with which it recently concluded a friendship treaty, to prevent the outbreak of full‐scale war.

A State Department official said the notes were sent Saturday and delivered today by the American ambassadors in the three capitals. In New Delhi, Ambassador Kenneth B. Keating delivered the President's message personally to Prime Minister Indira Gandhi at a 30‐ minute meeting.

Joseph S. Farland, the Ambassador in Islamabad, also conveyed Mr. Nixon's message directly to the Pakistani President, Agha Mohammad Yahya Khan. In Moscow, Ambassador Jacob D. Beam handed the note to the Soviet Foreign Minister, Andrei A. Gromyko.

Delivery Confirmed

Charles W. Bray 3d, the State Department spokesman, confirmed the delivery of the messages and said that the United States intended to continue to pursue its private efforts to avert an all‐out war. He indicated that the United States would not take the issue to the United Nations Security Council at this time.

“Our belief, as of this moment, is that quiet diplomacy involving a number of countries may be most useful,” Mr. Bray told reporters at the daily departmental briefing.

He added that the Presidential messages were part of this process and reflected “our very deep concern about the situation in South Asia.”

Speaking privately, United States officials said that the military situation along the border had deteriorated in the last few days. They said that despite the Presidential messages, the possibility of an all out war between the two nations could not be ruled out.

The officials said they had no way to confirm specific re ports of casualties, but that both sides had suffered losses in a series of sporadic engagements along the East Pakistani Indian border. They said they assumed that the casualties had been “in the hundreds, but not thousands” of men.

Mr. Nixon's weekend message to Pakistan is the latest in a series of Administration efforts to persuade the Government of President Yahya Khan to take deliberate steps to defuse the crisis. The note reportedly reiterated the United States view that the Pakistani Government ultimately will have to reach some sort of political accommodation with the Bengali independence movement.

United States officials also have been in touch with the leaders of the Bengali rebels recently in India in an effort to explore their views on a possible political settlement. The Bengali attitude was said to have “hardened” as a result of the increased support the rebels have received from India in re cent weeks.

Because of this. United States officials said they regarded the chance of an immediate com promise between the rebels and the Yahya Khan Government as “slight.”