Thousands of terrorized families driven from their homes by a second earthquake set up camp in the streets of Mexico City today as death toll estimates climbed to more than 10,000 and reports began to come in from areas closer to the quake epicenter indicating a wide swath of devastation and casualties.

As officials in the capital ordered mass burials to dispose of the dead, scattered looting and fighting for scarce water were reported around the city, and the hardest-hit areas went without electricity for the third day. Long lines formed at water mains that continued to flow. Officials reported that hoarding of food also had begun in some neighborhoods for the first time since the Mexican capital was hit Thursday morning by the most devastating earth tremor in its history.

U.S. Ambassador John Gavin said after making a helicopter trip over the city that at least 10,000 persons had been killed. He suggested that the final toll could rise to twice that figure as rescue workers continued dragging bodies from demolished buildings, and the extent of the damage becomes clearer.

At a news conference, he said at least five Americans had been killed in the disaster, including a man and a woman who died when the downtown Hotel Regis collapsed. The U.S. Embassy declined to reveal their names until the next of kin have been notified.

President Miguel de la Madrid's government has yet to release an official death toll estimate, but officials have said 2,000 bodies have been recoverd, and the count could rise to 5,000 in the capital area. Rescue workers have underlined the difficulty in determining how many bodies -- or living victims struggling to stay alive -- remain trapped beneath the mounds of cement rubble that dot the city.

Unofficial reports from the less populated states of Colima, Guerrero, Jalisco and Michoacan spoke of hundreds killed there and more injured.

The second earthquake, which struck here last night at dinner time with a force of 7.3 on the Richter scale, collapsed another 30 buildings that had been damaged earlier, Mexican officials said. It killed scores of persons who had lain trapped under rubble but had been clinging to life for 36 hours since the first wave of destruction hit.

The psychological impact of the second earthquake, here as in the outlying areas, seemed to be strong even if the overall destruction and loss of life it inflicted was much less than the first. Tens of thousands of Mexico City residents who had remained in damaged buildings after the first tremor dragged belongings into the street and remained outside. Some took refuge in parks or stadiums, where they were tended by rescue workers; others drove out of the city to stay with relatives.

"I'm not going back inside," said a woman carrying clothes and blankets into a park. "I can't, I refuse."

One family sat with its household belongings on the sidewalk within a circle defined by string tied to a lamppost. In a middle-class neighborhood near the hotel district, members of another family were hauling possessions from their damaged apartment into a car waiting below to carry them out of the city.

"We've got to go now," the father said, "the columns are starting to crack."

"The second one was more scary because you knew what had happened (in the first quake)," said Jack Novak of Alexandria in a call to The Washington Post, as he described scenes of people piled on flatbed trucks trying to leave the city and "the eerie sound of ambulances all night long. People were sleeping in the streets . . . . Complete condominiums fell over."

Novak said rescue workers were laboring with their bare hands and carrying rolls of wallpaper and draperies with which to pick up the dead.

Ambulances screamed through the city for the third day in a row as more wounded were uncovered. As the number of dead piled up, rescue officials deposited bodies in several locations and gave orders -- after photographs and dental imprints were taken for possible identification purposes -- for four mass burials and cremations today to prevent health hazards.

Rescue workers, many of them volunteers, also raced about the city with red flags flying on their cars to clear traffic. Red Cross, government officials and volunteers distributed blankets and first aid equipment to the thousands of families driven from their homes.

"Have patience," de la Madrid said in a televised message last night. "Unfortunately, in the face of an earthquake of this magnitude, we don't have the means to deal with this as quickly as we would like."

The number of Americans killed could rise from the five reported by Gavin, observers here said. The three Americans who have been identified by the State Department are Mary Elizabeth Vallejos and her two children, of Nebraska.

A number of Americans also were injured, according to a State Department spokesman in Washington, who said their names were not being released until their families were notified.

Gavin said the U.S. Embassy believes that there were about 4,500 American tourists around the capital this week in addition to the 138,000 U.S. citizens living in the sprawling Mexico City area, the world's largest urban conglomerate with more than 17 million inhabitants. More than 120,000 other Americans live elsewhere in Mexico, according to the State Department.

In Washington, President Reagan announced that his wife Nancy will fly to Mexico on Monday to express U.S. support for its neighbor to the south and to explore what kind of aid is most urgently needed. U.S. and Mexican officials urged donors to give cash rather than food and clothing to relief agencies channeling aid to Mexico.

A U.S. Air Force C5A Galaxy transport plane flew into the undamaged Mexico City airport this afternoon with firefighting helicopters and a demolition crew to blow up damaged buildings that are in danger of falling, Gavin announced.

Gavin said a suggestion that helicopter cranes be dispatched from the United States to lift away debris was rejected because with the city's 7,800-foot altitude they would be unable to operate efficiently.

The Mexican government, with strong national pride, traditionally has been reluctant to seek assistance for natural disasters. But officials said aid from the United States, Latin America and Europe as well as the United Nations was on the way.

Mexico "has not asked for aid, but we cannot refuse to accept it," said Foreign Minister Bernardo Sepulveda, the government's foreign-relief coordinator.

Argentina, Ecuador and the Dominican Republic sent planeloads of food, clothing and medicine, officials reported, and President Jose Sarney of Brazil was scheduled to arrive with an air shipment of aid from his country. Belgian doctors also were scheduled to arrive to help Mexican doctors working to save earthquake victims in makeshift medical facilities.

Two of the city's largest medical facilities collapsed in Thursday's tremor that measured 7.8 on the Richter scale -- the 12-story Juarez Hospital and the Centro Medico -- killing more than 100 doctors and at least 1,500 patients.

The Associated Press added the following:

At the Juarez Hospital, a rescue worker said, "We know we have a pocket of a least 10 people alive in this rubble."

At times, rescue workers asked the crowd gathered beside the flattened building to be quiet so that they could hear cries from those inside. "Is anyone there?" they yelled into small passages through the debris.

"You hear voices everywhere," said one intern who was helping tear down a small building that she said would be removed to help enter the remains of the demolished hospital tower.

Dr. Juan Aguilar Rodriquez said the rescue squads "are making tunnels and reaching them (the victims) with water, analgesics and some liquid food."