The airline already has daily flights to Washington's Dulles airport from Addis Ababa, with nonstops heading to Africa. But because of the capital's 7,700-foot elevation, flights heading to Washington stop in Rome and would stop in Dublin for Los Angeles.
"It's a very tough challenge for engines, for pilots," Gebremariam said. "The 777ER is the longest-range airplane in the world, but even then it cannot make it from Addis to Washington. It is flying from Addis to Beijing."
The airline has quadrupled in size during the last decade, with 68 planes flying to 18 domestic airports and 82 international destinations on five continents.
TODAY IN THE SKY: Ethiopian Air becomes 1st outside Japan to fly Dreamliner (August 2012)
PHOTOS: See what it was like to be on Ethiopian Airlines' Dreamliner delivery flight
Gebremariam was Washington for the U.S.-Africa Leaders Summit, where he called announcements of $33 billion in public and private U.S. investment in his continent "very encouraging."
"Of course, we have isolated problems here and there," Gebremariam said. "But overall the continent is doing well. The growth is very impressive."
He acknowledged the challenges of dealing with the Ebola outbreak in West Africa and avoiding conflict zones around the globe. But he said Africa is a popular and growing tourist destination with attractions such as Mount Kilimanjaro and Serengeti National Park.
"We encourage American tourists to visit," Gebremariam said, where the entire continent is just a connecting flight away. "You will be connecting to 49 destinations all over the continent in a couple of hours."
While some airlines have scrapped flights to nations struggling to contain Ebola, Ethiopian Airlines doesn't fly directly to three countries hit hardest by the outbreak: Guinea, Sierra Leone and Liberia. The outbreak has killed nearly 900 people so far in those nations.
Gebremariam said the airline is taking precautions urged by the World Health Organization to monitor passengers and crew members, and preparing a quarantine area in case a sick passenger arrives.
"We are taking all the precautions," he said. "Fortunately we don't fly to those affected places."
Ethiopia is surrounded by conflict zones, however. The Federal Aviation Administration has warnings for U.S. airlines about portable anti-aircraft weapons in Kenya, with suggestions to fly at least 20,000 feet above Somalia, at least 15,000 feet above Congo and 24,000 feet above Mali and Egypt's Sinai.
The concerns were revived with the shooting down July 17 of a Malaysia Airlines flight over Ukraine. The FAA banned U.S. flights to Israel's airport in Tel Aviv for about 36 hours because of threatening rockets from Gaza.
The International Air Transport Association, which represents 240 airlines worldwide, and the International Civil Aviation Organization, a branch of the United Nations that recommends policies, are developing standards for better warnings about where commercial airliners should avoid flying.
"We are trying to stay away from these places," he said. "Fortunately all our European flights go through Egypt, so they avoid Syria, Iraq and Ukraine. We don't fly over Libya, although it's a little more costly to avoid Libya on some flights."
As a precaution, the airline suspended a couple of flights to Tel Aviv, where Gebremariam was attending a meeting during the crisis. But flights resumed after assurances from the Israeli government, he said.
"It seems to be getting better now," he said.
TODAY IN THE SKY: Ethiopian Airlines 787 returns to service after repair (January 2014)
MORE: Dreamliner lauded as Ethiopian Air reports record profit (September 2013)
USA TODAY: Empty 787 catches fire, hits Boeing with new setback (July 2013)
In July 2013, a setback for the airline was a fire aboard a parked 787 Dreamliner at London's Heathrow airport, which was repaired and returned to service in December.
"We are satisfied with the repair and we are also satisfied with the Dreamliner," he said. "Now things are going well. We are using them about 14 hours a day, which is very high by any airline standard."
Passengers like the larger windows, less noise and the higher humidity in the cabin, which over longer flights reduces jet lag and fatigue, Gebremariam said.
"When it takes off, the lift is amazing," he said.