(CNN) -- A 21-year-old man from Kosovo is in custody after two U.S. airmen were killed and two others were wounded Wednesday in a shooting incident on a U.S. military bus at Germany's Frankfurt Airport, authorities said.

The suspect is named Arid Uka, from the northern town of Mitrovica, Kosovo's interior minister, Bajram Rexhepi, told CNN, citing the U.S. Embassy in Pristina as his source.

Uka approached the bus, which was parked outside Terminal 2 and was clearly marked as a U.S. military vehicle, German police said. He first engaged U.S. military members in a conversation, then pulled out a handgun and began firing -- first outside the bus and then inside the bus, police said.

He then fled, making it into the terminal, where he was taken into custody by German federal police, according to police.

Uka has passports from Germany and from Yugoslavia, the latter of which was issued prior to Kosovo's declaration of independence from Serbia in 2008, Rexhepi said. Officials were running a background check on Uka, who lives in Germany, for possible terrorist links, he said.

"It's either a terrorist act or he's crazy," Rexhepi said. "There cannot be any other reason."

CNN was not able to reach anyone at the U.S. Embassy for comment.

A U.S. military official said the bus driver was among the dead. Both fatalities were U.S. Air Force airmen from Lakenheath base in Britain, the official said.

The two wounded were security forces who were on their way to a deployment, said the source, who did not want to be identified because he was not authorized to speak publicly about the incident. He would not say to where they were to be deployed.

U.S. President Barack Obama told reporters he was "saddened and outraged" by the attack. "We will spare no effort in learning how this outrageous attack took place," he said, adding that the United States is working with German authorities.

"We don't have all the information yet, and you will be fully briefed when we get more information, but this is a stark reminder of the extraordinary sacrifices that our men and women in uniform are making all around the world to keep us safe, and the dangers that they face all around the globe," Obama said.

Police said they believe the suspect stormed onto the bus, which was waiting at the terminal, and began shooting.

"There was an incident today where two American soldiers were killed at Frankfurt airport," German Chancellor Angela Merkel said. "We don't know the details but I would like to say how upset I am."

She expressed her condolences to the soldiers' families and stressed that Germany will "do everything we can to try and find out quickly what happened."

Philip Murphy, U.S. ambassador to Germany, said in a statement he was "grateful for the assistance provided by German government officials in protecting U.S. servicemen and women, and in investigating this terrible act. In dificult times, Germans and Americans support each other."

FBI agents were on the scene shortly after the shooting occurred, said Tom Fuentes, a former FBI assistant director and CNN. The FBI's main office in Germany is in Berlin, he said, but it has a suboffice in Frankfurt.

The offense is a federal crime both in the United States and in Germany, he said, and could be prosecuted in either location, although that will be determined later. However, the investigation will meet U.S. constitutional standards, he said.

Authorities will be investigating the suspect's background and associates, likely subpoenaing telephone and e-mail records, Fuentes said.

Frankfurt is "the main hub of Europe," he said, and "the gateway to the Middle East." There have been terrorist plots in the past to attack U.S. servicemembers on the Ramstein base or elsewhere nearby, he said. "All of those are possibilities of what motivated this particular person."

CNN's Frederik Pleitgen, Ashley Hayes and Barbara Starr contributed to this report