* Haiti signs memorandum with U.S. govt
* Teams in place to prioritize relief, flights
* U.S. says no fuel at airport, some flights diverted
(updates with handover agreement, details on airport plan)
WASHINGTON, Jan 15 (Reuters) - Haiti gave the United States control of its main airport on Friday to bring order in the skies to aid flights from around the world and speed relief to the quake-traumatized Caribbean nation, the Obama administration said.
U.S. State Department spokesman P.J. Crowley told reporters that Haitian Prime Minister Jean-Max Bellerive signed a memorandum of understanding formally transferring operations at Toussaint L'Ouverture International Airport in Port-au-Prince.
"Obviously we will assume this responsibility as long as it's appropriate and to the point where the Haitian government is able and ready to resume that capability," Crowley said.
U.S. Secretary of State Hillary Clinton was due to visit Haiti on Saturday.
The modest airport became a bottleneck almost immediately after Tuesday's devastation as the world rushed help to the impoverished nation. Regional authorities believe as many as 200,000 people were killed in the quake.
Waves of military and civilian planes loaded with food and water, medicine, and rescue crews poured into the small Haitian air space but many flights circled for hours before landing or were diverted.
While a 9,000-foot runway can handle the biggest jetliners arriving "heavy" with cargo and the tarmac escaped serious damage, the Port-au-Prince airport was compromised by a severely damaged control tower and limited facilities for dealing with the relief effort.
The U.S. Air Force landed on Wednesday and immediately worked with Haitian authorities and a team from the Federal Aviation Administration to restore navigation and communications capabilities. They also sorted planes on the ground and began to organize arrivals.
But Haitian air space remained off limits through Friday to many flights approaching from overseas with little notice. Some planes bound for Haiti were diverted to the Dominican Republic and airports in Florida, the FAA said.
Aviation authorities were concerned that long approach delays could jeopardize onboard fuel supplies. Further complicating matters, the Port-au-Prince airport ran out of fuel, meaning any planes that landed would not be able to refuel for departure.
U.S. President Barack Obama said the United States, and countries including Brazil, Mexico, Canada, France, Colombia, Russia, Japan, and Britain managed to fly in rescue and logistics personnel and supplies. While some aid was getting in, the White House hoped improved logistics would streamline and accelerate the effort.
On Friday night, a ban was lifted on most flights heading for saturated Haitian air space. It was replaced by a two-tier approach for managing traffic that was worked out by international aviation authorities and Caribbean states.
Working with Haitian authorities, a team of U.S. military and civilian aviation experts began prioritizing arriving flights based on what was needed most on the ground.
A second team based at a U.S. military facility in Florida lined up airborne flights for arrival. Pilots are required to file a flight plan before departure and obtain a landing time. The window is open for 40 minutes - 20 minutes before scheduled arrival and 20 minutes after, an FAA advisory said.
Commercial flights have been banned since Tuesday. U.S. carriers serving Haiti include American Airlines and Spirit Airlines. American had been scheduled to fly in relief supplies.