Port-au-Prince, Haiti (CNN) -- Hundreds of thousands of people have died in Haiti's earthquake, the prime minister told CNN Wednesday. Haitian authorities said the powerful quake destroyed most of the capital city of Port-au-Prince. A top envoy called it a "major catastrophe."
Haiti's first lady, Elisabeth Debrosse Delatour, reported that "most of Port-au-Prince is destroyed" and that many government buildings had collapsed, Haiti's ambassador to the United States, Raymond Joseph, told CNN Wednesday morning. Delatour said President René Préval was all right, Joseph reported.
Rescue crews were racing Wednesday morning to fully assess the damage in the teeming hillside city, where toppled buildings killed and injured an untold number of people and trapped others in the rubble.
The U.S. State Department has been told to expect "serious loss of life," spokesman P.J. Crowley said, though precise casualty estimates were not immediately available. About 3 million people -- one-third of Haiti's population -- were affected by the quake, the Red Cross estimated. Authorities braced for civil disturbances.
Edmond Mulet, the U.N. assistant secretary-general for peacekeeping operations, told CNN that the National Penitentiary collapsed and the inmates escaped, prompting worries about looting by escapees.
President Obama pledged Wednesday that the U.S. government would lead "a swift, coordinated and aggressive effort to save lives" in Haiti after the earthquake.
"For a country and a people who are no strangers to hardship and suffering, this tragedy seems especially cruel and incomprehensible," he said.
The president noted that "military overflights have assessed the damage" from the earthquake and that civilian disaster assistance team were beginning to arrive in Haiti.
Obama said U.S. relief efforts are currently focused on a quick accounting of U.S. Embassy personnel and their families in Port-au-Prince, as well as other American citizens living and working in Haiti. He urged Americans trying to locate family members in Haiti to telephone the State Department at 888-407-4747.
The main airport in Haiti appears to be operable. U.S. Embassy staff at the airport said the tower and the lights are working, Crowley said Wednesday.
The quake ripped apart buildings, shearing huge slabs of concrete off structures in the poorest country in the Western Hemisphere. Many buildings that remained standing were left open to the elements, pictures from the scene showed.
First rescuers on the scene were often local people trying to help dig people out of the rubble by hand or to comfort injured survivors.
Pictures from Haiti showed concrete buildings that had fallen onto themselves, broken and flattened. People in the streets were dusty from the concrete and in some cases bloody from their injuries.
"One woman, I could only see her head and the rest of her body was trapped under a block wall," said Jonathan de la Durantaye, who drove through Port-au-Prince after the quake. "I think she was dead. She had blood coming out of her eyes and nose and ears."
The 7.0-magnitude earthquake struck shortly before 5 p.m. Tuesday, centered about 10 miles (15 kilometers) southwest of Port-au-Prince, the U.S. Geological Survey reported. It could be felt strongly in eastern Cuba, more than 200 miles away.
Many of the concrete-block homes in Port-au-Prince are built "helter-skelter, all over the place," Joseph said. The earthquake damaged buildings as grand as the National Palace, pancaking scores of structures, trapping people inside those buildings, and knocking down phone and power lines.
Former U.S. Ambassador to Haiti Timothy M. Carney told CNN that Port-au-Prince was particularly at risk because it grew rapidly from a population of about 250,000 in the mid-1950s to more than 2 million today, all with little oversight.
More than 100 employees of the United Nations' mission in Haiti were unaccounted for Wednesday after the earthquake, U.N. officials said.
Among the missing were the chief of the U.N. mission in Haiti and the agency's deputy special representative, U.N. Secretary-General Ban Ki-moon told reporters in New York.
The destruction included the U.N. peacekeeper compound, a five-story building where about 250 people work every day.
Three Jordanian peacekeepers died and 21 were injured, according to Jordan's state-run Petra News Agency. An Argentine member of the peacekeeping team also is confirmed dead, the Argentine military said.
Joseph Serge Miot, the archbishop of Port-au-Prince, died in the quake, according to the official Vatican newspaper.
None of the three aid centers run by Doctors without Borders in Haiti is operable following the earthquake, the group said Wednesday.
The group is focusing on re-establishing surgical capacity so it can deal with the crushed limbs and head wounds it is seeing, said Paul McPhun, an emergency management expert for Doctors without Borders.
CNN's Anderson Cooper, viewing Port-au-Prince from a helicopter, called the sight of the destroyed buildings in the quake-devastated city "incredibly shocking" and "eerie."
He said many people are "just kind of standing around on the streets, not really sure what to do or where to go, and for many, there is nowhere to go."
The disaster is the latest to befall the country of about 9 million people, roughly the size of Maryland, which is the poorest in the Western Hemisphere and among the poorest in the world.
Hurricane Gordon killed more than 1,000 people in 1994, while Hurricane Georges killed more than 400 and destroyed most of the country's crops in 1998. And in 2004, Hurricane Jeanne killed more than 3,000 people even as it passed north of Haiti, with most of the deaths in the northwestern city of Gonaives.
Gonaives was hit heavily again in 2008, when four tropical systems passed through.
With people cutting down trees for fuel and to clear land for agriculture, the mountainous countryside has been heavily deforested. That has led to severe erosion and left Haitians vulnerable to massive landslides when heavy rains fall.
Haiti shares the island of Hispaniola with the Dominican Republic. Buildings shook in the Dominican capital, Santo Domingo, during the earthquake, but no major damage was reported there, according to The New York Times.