Esper said that he gave his consent to Gen. Scott Miller, commander of U.S. and NATO forces in Afghanistan, for reducing the number of U.S. troops in the country from about 12,000 to about 8,600, beginning in about 10 days.
"My instruction to the commander was: 'Let's get moving. Let's show our full faith and effort to do that,'" Esper said.
An agreement between the insurgent Taliban and the United States was signed on Saturday. It calls for a U.S. troop reduction in 135 days and total withdrawal of U.S. forces in 14 months.
The Taliban must meet specified security requirements, though, and the treaty may already be unraveling. Following a week of relative calm, a Taliban attack killed three people and injured 11 at a sports event in Afghanistan, an indication that the group has not entirely pulled back from use of violence.
The United States "will closely watch the Taliban's compliance with their commitments, and calibrate the pace of our withdrawal to their actions," said U.S. Secretary of State Mike Pompeo, who attended the signing in Doha, Qatar, on Sunday.
Esper, in Washington on Monday, said he expects that Taliban violence will "decrease over time as we move forward. This is going to be a step-by-step process and we'll evaluate every day."
Joint Chiefs of Staff chairman Gen. Mark Milley, speaking alongside Esper, agreed.
"I would caution everybody to think that there's going to be an absolute cessation of violence in Afghanistan, that is probably not going to happen," Milley said.