Esper said that in addition to negotiating with the Taliban, he has been consulting with allies about the proposal at NATO headquarters in Brussels.
"We've had a series of bilateral and collective meetings about the path forward," he said. "We've said all along the best if not only solution in Afghanistan is a political agreement. Progress has been made on this front and we will have more to report on that soon, I hope."
He added that the seven-day time period will rely on the Taliban meeting certain conditions.
"It is our view that seven days, for now is sufficient, but in all things, our approach to this process will be conditions-based," Esper said. "I will say it again: conditions-based so it will be a continual evaluative process as we move forward, if we move forward."
Last month, U.S. envoy for Afghan reconciliation Zalmay Khalilzad said the United States had reached an "important stage" in talks for an agreement on a short window in which the Taliban would commit to reducing violence.
While far short of the complete cease-fire sought by the Afghan government, such a commitment would still represent a key development in the talks that are ultimately aimed at removing U.S. forces from Afghanistan, where they have been stationed since late 2001.
On Thursday, Esper said the United States was confident it can reduce the number of troops in the country by about a quarter in the first phase of withdrawal of the 12,000 to 13,000 troops.
"We have said consistently based on the recommendations of the commanders in the field that we are comfortable going down to an 8,600 number because we are confident we can accomplish our tasks at that number," he said.
President Donald Trump called off negotiations in September following a Taliban attack in Kabul that killed an American soldier. He allowed them to resume after a surprise Thanksgiving trip to visit troops at Bagram Airfield.