Taliban Suicide Bomber Kills 4 Americans in Attack on Bagram Airfield

— -- Four people were killed and 17 others were injured in a deadly Taliban suicide bomb attack inside Bagram Airfield, the large U.S. military base in Afghanistan.

"I am deeply saddened to learn that an explosion early this morning at Bagram Airfield in Afghanistan has resulted in U.S. casualties," said Defense Secretary Ash Carter in a statement today.

"An apparent suicide bomber has taken the lives of two U.S. servicemembers and two U.S. contractors working on the base," said Carter. "The explosion wounded 16 other U.S. servicemembers and one Polish soldier participating in our NATO mission."

He added: "I want to express my sincere condolences to the families of the fallen, and I want to reassure the loved ones of those injured that they are getting the best possible care."

A U.S. official said the attack occurred inside the base and the attacker wore a suicide vest. The blast occurred as the military personnel were moving between morning physical exercises and a dining hall, according to the official.

The official also said that one thing being looked at is whether the bomber was someone who worked at the base or whether the bomber infiltrated security at the base.

Carter said that force protection for the 9,800 American troops in Afghanistan "is always a top priority, and we will investigate this tragedy to determine any steps we can take to improve it."

"For those who carried out this attack, my message is simple. We will not be deterred in our mission to protect our homeland and help Afghanistan secure its own future," said Carter.

The attack occurred at just after 5:30 a.m., according to the NATO-led Resolute Support Mission.

The Taliban have claimed responsibility for the attack, which they said was carried out by a suicide bomber.

Zabiullah Mujahid, a Taliban spokesman, said the bomber managed to enter the base with explosives and detonate himself among American servicemembers who were in the midst of doing their morning exercise.

General John W. Nicholson, commander of Resolute Support for the U.S. Army, said in a statement, "To the family and friends of those who lost their lives today, we share your loss and our thoughts are with you. We offer you our deepest condolences. For the family and friends of those wounded in today’s attack, let me assure you they are receiving the best care possible, and we will keep them in our thoughts today."

He added: "To those who target Coalition forces, ANDSF, and Afghan civilians, Resolute Support and USFOR-A will continue to pursue our Train, Advise, and Assist mission to help our partners create a better Afghanistan."

ABC News' James Meek and Aleem Agha contributed to this report.