PORT-AU-PRINCE, Haiti (AP) — Desperately needed aid from around the world slowly made its way Thursday into Haiti, where supply bottlenecks and a leadership vacuum left rescuers scrambling on their own to save the trapped and injured and get relief supplies into the capital.

The international Red Cross estimated that 45,000 to 50,000 people were killed in Tuesday’s magnitude-7.0 earthquake.

President Barack Obama announced that “one of the largest relief efforts in our recent history” is moving toward Haiti, with thousands of troops and a broad array of civilian rescue workers flying or sailing in to aid the stricken country – backed by more than $100 million in relief funds.

To the Haitians, Obama promised: “You will not be forsaken.”

The nascent flow of rescue workers showed some results: A newly arrived search team pulled U.N. security worker Tarmo Joveer alive from the organization’s collapsed headquarters, where about 100 people are still trapped. He stood, held up a fist in celebration, and was helped to a hospital.

There are easily hundreds, and perhaps thousands, of people trapped, living or dead, in collapsed buildings.  No one knows for certain.  Friends and relatives have had to claw at the wreckage, often with bare hands, to try to free them.

Many dead bodies that were recovered still lay in the street, often covered by a white cloth, in 81-degree heat.

Some people dragged the dust-covered dead along the roads toward the morgue, where people came to hunt for relatives in a macabre sea of hundreds of bodies just a few feet from where badly injured victims awaited a doctor from the neighboring hospital.

Planes from China, France, Spain and the United States landed at Port-au-Prince’s airport, carrying searchers and tons of water, food, medicine and other supplies – with more promised to the Western Hemisphere’s poorest nation. The Red Cross has estimated 3 million people – a third of the population – may need emergency relief.

The flow into the capital’s damaged airport was so great that the Federal Aviation Administration halted all civilian flights from the United States to Port-au-Prince for a time Thursday because there was no room on the ground for more planes and not enough jet fuel for planes to go back, an official at the FAA said, speaking on condition of anonymity because he was not authorized to talk publicly. Civilian relief flights were later allowed to resume.

It took six hours to unload a Chinese plane due to a lack of equipment – a hint of possible bottlenecks ahead.

“We don’t have enough handling equipment or the people to run it,” said U.S. Air Force Col. Ben McMullin, part of the team handling traffic at the airport. “We’re trying to control the flow of aircraft.”

In Geneva, Red Cross spokesman Jean-Luc Martinage said the Haitian Red Cross estimated 45,000 to 50,000 people were killed, based on reports from its volunteers in Port-au-Prince.

There seemed to be little official Haitian presence in much of the capital – or at the airport, where the U.S. Southern Command was controlling flights from a fenced-off building at the end of the runway. The facility’s usual tower had collapsed.

McMullin said about 60 planes carrying 2,000 people had landed between Wednesday, when the airport reopened, and noon Thursday.

U.S. military forklift operators helped unload some foreign flights as well as U.S. cargo, and Haitian staff were far outnumbered by foreign aid workers and military. No senior Haitian officials were visible.

Since the earthquake, President Rene Preval has maintained his typical low profile, granting only a couple of media interviews and making few public appearances. His official palace and home were damaged in the quake and the Parliament building collapsed, along with some other ministries and departments.

State Department spokesman P.J. Crowley said the U.S. had been in touch with Preval, and added: “We’re not taking over Haiti. We are helping to stabilize Haiti, we’re helping to provide them lifesaving support.”

The often-chaotic capital was surprisingly calm, despite the devastation, though journalists occasionally heard the sound of isolated gunfire. It was not clear if it was aimed at people. Even in normal times, guards sometimes fire shotguns in the air to keep people away from stores.

There has been widespread looting of collapsed buildings since the earthquake hit, but rarely of undamaged shops, said Matt Marek, Haiti country representative of the American Red Cross.

“There is no other way to get provisions,” he told The Associated Press.  “Even if you have money, those resources are going to be exhausted in a few days.”

But some other aid groups expressed increasing concern about security.

“It is dangerous at night. Lootings were widespread and some markets were ransacked,” Oxfam spokesman Cedric Perus said in a statement.

Some people buried loved ones in shallow graves on the side of a road. A woman was strapped to a board and covered with a sheet before burial, as the mourners lit fires to keep away flies and cover the stench.

Others tried to carry the dead to nearby hills for burial, prompting Brazil’s military – the biggest contingent among U.N. peacekeepers – to warn that the practice could lead to an epidemic. It said it asked authorities to create a new cemetery.

The Brazilian military said it also was worried that bodies could be left too long because many Voodoo followers in Haiti do not allow the dead to be touched before all their rituals are concluded.

There was damage outside the capital, too. In the port of Jacmel to the south, about 3,000 people forced from their homes slept overnight on the runway of an airstrip, said Yael Talleyrand, a high school student interviewed by e-mail and instant message.

“I almost cried, because so much people were crying, praying and I had never seen this in my entire life,” said Talleyrand, whose parents run an economic development and health foundation.

Aid workers reported confusion over how to cope with the sudden flood of aid from scores of places.

“Donations are coming in to the airport here, but some are coming without notice from very well-meaning groups,” said Save the Children spokeswoman Kate Conradt. “There is not yet a system to get it in” to those who need it.

Obama promised Haitians an all-out rescue and humanitarian effort, including the military and civilian emergency teams from across the U.S., adding that America – and the world – “stands with you.”

As many as 5,500 U.S. infantry soldiers and Marines will be on the ground or on ships offshore by Monday, a Defense Department official said. More than a half-dozen ships were en route or preparing to get under way, said spokesman Bryan Whitman. They included the aircraft carrier USS Carl Vinson, to arrive Friday, and a hospital ship with 12 operating rooms, the USNS Comfort, expected by Jan. 22.

The U.S. Army said more than 100 soldiers from the 82nd Airborne Division were heading out from Fort Bragg in North Carolina, looking for locations to set up tents and other essentials in preparation for the arrival of another 800 personnel Friday.

French Foreign Minister Bernard Kouchner said that 91 injured French nationals were evacuated to the Caribbean island of Martinique.

About 3,000 police and international peacekeepers cleared debris, directed traffic and maintained security. But law enforcement was stretched thin even before the quake and would be ill-equipped to deal with major unrest.  The U.N.’s 9,000-member peacekeeping force sent patrols into the streets while securing the airport, port and main buildings.

U.N. Secretary-General Ban Ki-moon said 36 of his organization’s personnel were confirmed dead and nearly 200 were missing – 100 in the rubble of its headquarters alone.

The State Department announced one American had died in Haiti, saying that at least 164 U.S. citizens have been evacuated since the quake.

Coast Guard C-130 planes have airlifted 42 American officials and their families and another 72 private citizens to safety, Crowley said.

Another 370 Americans were awaiting flights out, he said. There were about 45,000 Americans living in Haiti at the time of the earthquake.

The International Committee of the Red Cross said it set up a Web site to help Haitians find missing loved ones. Robert Zimmerman, deputy head of the group’s tracing unit, said people in Haiti and abroad can register missing relatives on the site.

Associated Press contributors to this story: Jonathan Katz, Jennifer Kay, Gregory Bull and Tamara Lush in Port-au-Prince; Edith M. Lederer at the United Nations; Frank Jordans and Bradley S. Klapper in Geneva; Jenny Barchfield in Paris; Pauline Jelinek in Washington; Tales Azzoni in Sao Paulo; and Adam Geller in New York.