President Augusto Pinochet appeared to face a worsening political crisis here today as street demonstrations continued for a third straight day and the Air Force publicly questioned government accounts of violence that left 20 persons dead and 62 wounded.

Following harsh repression Thursday by 18,000 police and troops who stormed university buildings and aimed stones, tear gas and automatic weapons fire at demonstrators, new protests erupted this afternoon at the state medical school campus and throughout southern Santiago.

Clashes between police and demonstrators were reported in several poor neighborhoods tonight, with one person shot and wounded in Santiago. A second person was said to have been wounded by police fire in the resort town of Vina del Mar. However, police appeared to have relaxed pressure on demonstrations and in many neighorhoods residents who built barricades were not challenged by security forces.

At the same time, Gen. Fernando Matthei, the commander in chief of the Air Force and one of four members of the military government junta, appeared to contradict official accounts that yesterday's deaths had resulted from confrontations between security forces and armed leftist militants.

In the most serious public sign of military discord in recent years, Matthei disclaimed responsibility of the Air Force for the killings and added that "it is time for us to come to an understanding with the political parties . . . . It is time for Chile to open a political debate. It is time that in Chile all the arguments in favor and against new solutions resurge and that the government knows them and that all Chileans can express themselves."

Sources here said that Matthei also privately expressed his dissatisfaction to several leaders of the government opposition and added that he had told Pinochet that the Air Force would not participate in further repression.

Following a 6:30 p.m. curfew yesterday in Santiago, declared by the local military command, several persons uninvolved in protests, including three children under the age of 10, were killed by gunfire. Widespread reports by witnesses said today that government forces had fired into the air and aimed both stones and bullets at apartment buildings and home windows in an effort to stop citizens who banged pots and pans in protest against military rule.

Witnesses said that at least four deaths, including that of an 8-year-old child, occurred when the victims were hit inside their homes by gunfire from government forces. The other two children apparently were victims of shots fired into crowds.

The death toll far exceeded the eight fatalities reported in the three previous national protests against Pinochet this year.

The State Department said Friday that it deplored the deaths and injuries in the confrontations in Chile. Spokesman John Hughes said: "We deplore the loss of life and the injured. We also regret that recent efforts to promote a dialogue, to avoid violence and to build a consensus have so far been unable to halt the process of polarization."

Hughes said the United States believed that Chileans from all sectors would have to find ways to overcome their differences, within a framework of respect for civil and human rights, "so that a real transition to democracy can take place as the vast majority of Chileans fervently seek."

Troops were withdrawn from the capital this morning, and today's demonstrations were answered by police using clubs and tear gas, according to initial reports. Unofficial reports said a number of persons had been arrested or injured near the medical school and in the southern residential area of La Legua.

Tonight, police surrounded La Legua, a poor working-class area, and battles were reported. The archbishop of Santiago, the Rev. Juan Fresno, made a public attempt to mediate in the conflict but received no immediate response from the authorities.

Opposition leaders, including a group of political figures known as the Democratic Alliance, had supported only one day of peaceful protests against Pinochet for Thursday. However, the Chilean Communist Party called for a three-day protest extending through today, and active resistance to security forces.

This morning, Army and government spokesmen did not dispute that most of the deaths and injuries had resulted from fire by security forces, but they said police and troops were acting defensively. Government General Secretary Alfonso Marquez de la Plata said at a press conference that nine soldiers had been injured by attacks and that armed groups had assaulted security forces.

Matthei, however, appeared to contradict that account today in describing his own visit to several poor neighborhoods and his flight over the city in a helicopter. Speaking to reporters, he said, "There was no one in the street. There were no confrontations in those neighborhoods."

Referring to the Air Force, Matthei added, "Our forces did not fire nor did they receive attacks of any kind."

The Air Force has been reported for some time by diplomats and political sources here to be dissatisfied with Pinochet's direction of the government. However, Matthei's statement was the first public indication of any differences.

There was no public sign here tonight that the Air Force had rebelled against Pinochet or that other military sectors shared Matthei's position. Pinochet, a general who serves both as president and commander in chief of the Army, technically responds to a four-member service junta but in practice he maintains his power largely through the Army.

The 67-year-old leader was challenged by the Air Force in 1978 but succeeded in ousting the man who was then its commander in chief, Gen. Gustavo Leigh, and nearly 20 other generals supporting Leigh.

One prominent retired Army general, Roberto Viaux Marambio, also appeared to question Pinochet sharply today. In a statement, Viaux said that "police action is not and will never be the proper role of the armed forces."

Viaux, a nationalist who led two military conspiracies against democratic governments in 1969 and 1970, also said, "I remind my comrades in the armed forces that their mission cannot depart from that of guarding the higher interests of Chile over every other consideration."

Viaux is not believed to retain widespread influence in the Chilean Army. However, there was speculation that his criticism was shared by active duty Army leaders. The strong government action against yesterday's demonstrations also drew harsh criticism from a range of public leaders and appeared to undermine a Cabinet sworn in by Pinochet Wednesday and pledged to political liberalization.

Gabriel Valdes, president of the Christian Democratic Party, said the violence "was the direct responsibility of the government for having used troops to maintain public order." He added that Pinochet's new Cabinet "demonstrated yesterday that they do not know how to manage public order."