WASHINGTON -- U.S. Special Operations Command are running the airport in Port-au-Prince coordinating distribution of relief and U.S. teams have pulled out about half of the survivors from under the rubble, but U.S. officials on Sunday insisted the Haitian government is in charge of the country after a devastating earthquake flattened the capital last week.

Repeating the mantra that the earthquake is a "disaster of epic proportions," Lt. Gen. P.K. Keen, the deputy commander of U.S. Southern Command, told NBC's "Meet the Press" that the U.S. military is "here in support of the government of Haiti working alongside the United Nations."

"We're not going to be running the country," Keen said.

"We're here at the invitation of the Haitian government," Denis McDonough, Deputy National Security Adviser to President Obama, told reporters later in the day. 

Rajiv Shah, President Obama's point man on Haiti as head of U.S. Agency for International Development, said the U.S. is working to assist Haitian President Rene Preval, whom President Obama could not reach for several days after the quake struck Tuesday afternoon.

"He asked us to be coordinated with him and to work with him -- and in response to his request to help provide services to the people of Haiti and to help rebuild Haiti in a specific way," Shah said.

But much of the relief and rescue operations are being led by U.S. and U.N. officials. Minustah, the U.N. Special Mission to Haiti, has 9,000 peacekeepers who are being redirected to humanitarian service. Keen said 1,000 U.S. forces are helping the mission on the ground and another 3,600 are working from naval vessels. By Monday, as many as 10,000 U.S. forces could be helping with relief efforts in Haiti. 

French Secretary of State for Cooperation Alain Joyandet reportedly filed a complaint with the U.S. State Department over the weekend saying that two French aid planes were turned away from the runway.

Tim Callaghan, senior regional adviser, Latin America and Caribbean from USAID's Office of Foreign Disaster Assistance, did not confirm receipt of the complaint, but said, "It's absolutely understandable that tempers would flare and that frustrations would come forth here and that's all being directed at improving the process to make sure things run smoothly."

Callaghan said U.S. Ambassador to the U.N. Susan Rice was headed up to the United Nations on Monday for a meeting of the U.N. Security Council to make sure "we're doing everything in close consultation with the Haitian government, and drawing on the established networks, nongovernmental organizations and others who've been working here really for years."

Keen noted that the U.N. and international community is working jointly from a "humanitarian coordination center" that is operational 24/7, and said nations like Brazil are working closely with the U.S. and U.N. on rescue and relief.

But Shah acknowledged that only a fraction of the food and water supplies are reaching Haiti at this point. 

"We've sent down 600,000 humanitarian daily rations. I think 130,000 of those were delivered by helicopter yesterday," he said, adding that 8 million daily rations will be needed in the "initial period."

"That's what the distribution system can handle. So we're really trying to address it in a comprehensive way and trying to get as many commodities, whether it's food or water, medical supplies, tents and tarps," Shah said.

So far the Pan American Health Organization has put the number of deaths caused by the earthquake at 50,000 to 100,000 people. Keen was hesitant to give an estimate on the human toll.

"I think it's too early to tell, but it's clear it is significant, and I do know that the United Nations forces are doing everything they can to support the government of Haiti" as it figures out how to dispose of mass fatalities, Keen said.

Col. Buck Elton, Commander, SOC South Haiti.said the Haitian police force was helping out "tremendously" with traffic control around the airport, and the airport has had no security incidents. 

As the mission moves away from rescue and toward resettlement of survivors, shelter experts will make recommendations to the Haitian government on the best way to house the tens of thousands who've lost their homes, Callaghan added. 

But as the situation grows more desperate, officials are keeping an eye on the ability of Minutsah and Haitian forces to keep order. 

"We don't discuss rules of engagement but we're here on a humanitarian effort and our military leadership as you heard on all the shows feel that they have all they need to ensure that this is done in the most secure fashion," McDonough said.