The United States has committed more than $265 million in equipment and training to the mission, Davis told reporters at the Pentagon.
The effort, which Congress approved in 2014, is to help Ukraine better monitor and secure its border, operate more safely and effectively, and preserve and enforce its territorial integrity, the spokesman said.
"This is part of our ongoing efforts to contribute to Ukraine's long-term military reform and professionalism, and to help improve Ukraine's internal defense capabilities and training capacity," Davis said.
The phase that began yesterday will train up to five battalions of Ministry of Defense personnel and one battalion of special operations forces personnel, he said. U.S. forces just completed training Ukrainian national guard forces.
About 300 U.S. soldiers from the 173rd Airborne Brigade are participating in the training, which is taking place in western Ukraine. NATO allies and other U.S. personnel are participating as well.
Davis said that in addition to the training, the United States will be working with the Ukrainian Ministry of Defense on a training center and other institution-level development.
The Ministry of Defense training will be conducted at the International Peacekeeping and Security Center at Yavoriv, and the special operations forces training will be conducted in Khmelnytskyi.