Watch live reports from Port-au-Prince, Haiti. Anderson Cooper is on the scene for firsthand accounts of the devastation from the earthquake.

Port-au-Prince, Haiti (CNN) -- Countries and aid groups large and small worked Thursday to help survivors in quake-ravaged Haiti in an international effort rivaling the response to the 2004 Asian tsunami.

People dug furiously to rescue loved ones from the rubble of Port-au-Prince as international aid groups scrambled to provide medical care, food and water to tens of thousands after Tuesday's devastating 7.0-magnitude earthquake.

President Obama on Thursday promised $100 million in immediate American relief aid to Haiti -- an amount he said would grow in the year ahead.

"One of the largest relief efforts in recent history" is en route to Haiti, he said at the White House. Elements of the U.S. military have been dispatched to the stricken Caribbean country and ensured its airport is operating, he added. The first waves of U.S. rescue and relief workers are "on the ground and at work," he said.

"To the people of Haiti, we say clearly and with conviction, you will not be forsaken," Obama said. "You will not be forgotten. In this, your hour of greatest need, America stands with you. The world stands with you."

Haitian airspace was opened Thursday to charitable organizations, enabling humanitarian aid to be flown in, a Red Cross official said. But the limited infrastructure in Haiti doesn't appear to be able to accommodate the flood of aircraft headed there.

One humanitarian flight from the University of Miami couldn't take off because it couldn't land in Haiti and another was hovering in the air above the country, CNN's Elizabeth Cohen reported in Fort Lauderdale, Florida.

U.S. Secretary of State Hillary Clinton called the next 24 hours "critical to save those lives that can be saved."

"Once we can get communications up so we can tell people where to go, what kind of help they can expect, we'll be able to better manage the crisis," Clinton said on CNN's "American Morning."

She said the United States is providing a communications network to shore up the battered Haitian government infrastructure.

People around the world have tapped into social media Web sites, such as Facebook and Twitter, to find out about survivors and keep up with the crisis.

Watch as rescue teams gear up for hard work

Clinton said $3 million had been raised through a State Department program in which individuals with U.S. cell phones can donate $10 to the Red Cross, by texting "Haiti" to 90999.

The quake affected roughly one in three Haitians -- about 3 million people, the Red Cross estimated. It was so strong that it was felt in Cuba, more than 200 miles away.

See CNN's complete coverage of the quake

Precise casualty estimates were impossible to determine. Haitian President Rene Preval said Wednesday he had heard estimates of up to 50,000 dead, but that it was too early to know for sure. The Haitian prime minister said he worries that several hundred thousand people were killed.

And Felix Augustin, the Haitian consul general to the United Nations, said more than 100,000 may have perished.

The death toll of U.N. personnel, including military and police officers, stands at 22, U.N. Secretary-General Ban Ki-moon said Thursday. About 150 U.N. staff members remain unaccounted for in the earthquake's aftermath, he said.

Search and rescue units geared up to save trapped people in the capital, where the quake pancaked houses and chased others out in the streets, prompting thousands to sleep out in the open on mattresses and cardboard boxes. Rubble-strewn roads, downed trees and a battered communications network hampered humanitarian groups trying to get supplies to victims.

Watch a heartbreaking tour of the devastation

The calamity has overwhelmed doctors. Clinton said Port-au-Prince hospitals have collapsed and the few facilities still open can't handle the needs of the injured. The United States and other countries were dispatching medical supplies, facilities and personnel, and Clinton said that will be a challenge.

"This is a large area involving many, many, many millions of people who have been cut off from access. Just getting to people to provide the medical assistance they need is proving to be very difficult," Clinton said.

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Clinton said the U.S. and other countries' search and rescue teams have begun their work in Port-au-Prince to search for the missing, from residents sandwiched in their homes and to others who are unaccounted for, including some members of the Haitian parliament, the U.N. peacekeeping force and Doctors Without Borders.

The overcrowded national penitentiary in the capital collapsed, and inmates escaped, prompting worries about looting, said Edmond Mulet, the U.N. assistant secretary-general for peacekeeping operations. But Haitian Prime Minister Jean-Max Bellerive said the population has remained relatively calm in the face of the disaster.

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Clinton said the United States is providing security help to the United Nations, which was devastated by the collapse of its headquarters, a peacekeeping and police force established after the 2004 ouster of then-President Jean-Bertrand Aristide.

"The authorities that existed before the earthquake are not able to fully function. We'll try to support them as they re-establish authority," Clinton said.

She said a contingent of 2,000 U.S. Marines will help the international peacekeepers who have served as police in Haiti, which doesn't have an army.

"We've got the 82nd Airborne and other military assets coming in. We had a military team reopen the airport so we can start to handle the big heavy planes," she said.

The United Nations announced $10 million in aid; the World Bank pledged $100 million. Agencies, celebrities and charities mobilized relief efforts, including the Samaritan's Purse, Islamic Relief USA, Jewish Federations of North America, Salvation Army, Catholic Relief Services, Jolie-Pitt Foundation and musician Wyclef Jean's Yele Foundation.

Watch as U.N. program vows more food aid

Belize, Brazil, Canada, Chile, China, Cuba, France, Guyana, Israel Iceland, Japan, Morocco, the Netherlands, Russia, Spain and the United Kingdom also offered aid.