PORT-AU-PRINCE -- Government workers dug mass graves and buried more than 7,000 dead Thursday as corpses overwhelmed this earthquake-ravaged city awaiting a surge of relief supplies amassing in Miami and elsewhere.

Thousands more corpses crammed hospitals and morgues still without electricity and communications two days after the massive 7.0-magnitude earthquake.

Casualty estimates were still unknown but the Haitian Red Cross in Port-au-Prince estimated the dead at 45,000-50,000, a figure reported in Geneva by spokesman Jean-Luc Martinage of the International Red Cross.

In portions of the city, the nauseating odor of the dead was inescapable.

"We need help, " said Rothin Massena, 29, a student who stood amid the wails of earthquake wounded outside a Petionville hotel. "Where is the international community for us? We don't have food. We don't have water. We don't have money."

President René Préval told The Miami Herald that in a 20-hour span, government workers removed 7,000 corpses from the streets and morgue and buried them in mass graves.

Still, thousands more awaited burial, a trail of dead along sidewalks from downtown to the hills of Petionville, many abandoned, some covered in sheets or carted through the streets on makeshift stretchers fashioned from wood and soiled mattresses.

"We cannot afford to wait on the international community, " said Dr. Ariel Henry of the Ministry of Health, describing the need to resort to landfill-style burials.

"We are out of hospitals. We don't even have electricity. And we don't even have supplies, " from syringes, antibiotics and painkillers to blood for transfusions.

Communications remained sporadic, if not gone, in most portions of the city of two million people. Haitians mostly fended for themselves, some still digging through the rubble of collapsed buildings, others searching for gasoline and water.

There was one bit of relief in the otherwise bleak news. Aftershocks tapered off to a mere four Thursday, compared to 37 in the aftermath of the massive quake that struck around 5 p.m. on Tuesday. A few rescue teams got in and scoured the rubble for survivors. Miraculously, at least two survivors were found, including Tarmo Joveer of Miami Shores. Joveer emerged after a U.S. search-and-rescue team dug for five hours through the wreckage of the six-story U.N. building. He pumped a fist of celebration after his rescue.

A United Nations security officer, Joveer was inside the building when it collapsed Tuesday, apparently entombing dozens of others, including the chief U.N. envoy to Haiti. Hédi Annabi, who was meeting with a Chinese delegation when the earthquake struck, remained missing Thursday.

In Washington, President Barack Obama announced "one of the largest relief efforts in our recent history, " starting with $100 million in aid.

Throughout the day, waves of desperation whipped survivors and wounded who heard help was on the way, saw helicopters fly over but wondered when it would arrive.

"We had a problem with the international coordination, " said Interior Minister Paul Antoine Bien-Aime, predicting a break in the bottleneck of relief flights as early as Friday. The flow of private charitable relief ground to a halt because the Federal Aviation Administration grounded most civilian U.S. aircraft and permitted only U.S. military flights to land at Port-au-Prince.

Water, syringes, tarps, tents, 45,000 pounds of beans and diapers from the American Red Cross and other charities lay stacked by the tons on pallets in warehouses across Miami-Dade and elsewhere. Other supplies also grounded included syringes, intravenous lines.

"Logistics is a crucial issue, " said State Department spokesman P.J. Crowley. "So we are trying to work to create a system where we get the planes stacked down on the ground, offload cargo, onload evacuees that might be going on it."

Thirty-one countries had offered assistance, he said, some still en route Thursday. But eight search-and-rescue teams were on the ground, from Iceland, Spain, Chile and the United States.

Miami-Dade's Fire Department Urban Search and Rescue Team and Rescue Team Task Force One, with 80 people and seven dogs, were among them. International relief from elsewhere was permitted to land, said Bob Appin at the U.S. Southern Command in Miami-Dade. But U.S. air cargo traffic was grounded to give the military airlift priority to bring moving equipment, yet to be disclosed, and the first 100 of a planned 900 paratrooper deployment of the 82nd Airborne Division from North Carolina.

While the runways were functional, cargo executives told The Miami Herald that the battered airport also lacked the equipment needed to unload massive freight pallets from the planes.

Some Miami aircraft headed for Haiti and found themselves diverted elsewhere.

"We had to hold for two hours, " said Christine Richard, marketing director for Amerijet, a Miami cargo company hired by relief agencies to deliver supplies. "We ended up landing in the Dominican Republic. . . . It's very frustrating."

Some aircraft managed to land in Port-au-Prince, however. American Airlines had two flights scratched and two landed from Puerto Rico as well as charters carrying Miami Fire and Rescue and a Fairfax, Va., County search and rescue team.

In Geneva, the International Committee of the Red Cross sent 40 tons of medical supplies -- and 3,000 body bags -- as well as experts on reuniting families separated by disaster in two flights. The shipment could arrive Friday at the earliest.

But for much of Thursday, Haiti was on its own.

At the Port-au-Prince morgue, Lionel Gaedi was confronted by a horrific scene outside when he went in search of the remains of his brother Josef.

Toddlers piled up on naked adults, some wrapped in sheets, others exposed to the blazing sun for a half-block outside the Port-au-Prince morgue.

Throughout the day, police, civilians and private clean-up companies dumped cadavers because they had no other place to take them.

The morgue had run out of room so people were left on the street, where family members like Gaedi walked among them in search of their lost loved ones.

Miami staff writers Charles, Daniel and Robles reported from Haiti. Rosenberg reported from Miami, as did staff writers Dan Chang, Douglas Hanks, Nancy San Martin and Jim Wyss. Lesley Clark contributed from Port-au-Prince.