Less than 24 hours after the agreement was signed, Afghan President Ashraf Ghani, whose government was not involved in the U.S.-Taliban deal, rejected the Taliban’s demand.

"The reduction in violence will continue with a goal to reach a full ceasefire,” he told reporters in Kabul. "There is no commitment to releasing 5,000 prisoners."

Senior Pentagon officials cautioned against jumping to conclusions just two days after the agreement was signed. Defense Secretary Mark Esper told reporters that officials are still working to get more information about the attack reported in Khost province on Monday that killed at least three people and wounded 11, even as the Taliban said Monday it was resuming its offensive against Afghan security forces.

Gen. Mark Milley, chairman of the Joint Chiefs of Staff, noted that multiple terrorist organizations are operating in Afghanistan — such as al Qaeda and ISIS — and it is not yet clear that the Taliban were responsible for the attack.

Milley also cautioned that there won't be “an absolute cessation” of violence in the country.

“It’s probably not going to go to zero,” he said.

Under the agreement, U.S. troops will begin withdrawing within 10 days, with the goal of reducing the footprint to 8,600 within 135 days. Esper said he did not know whether the drawdown has “actually, physically begun” —although President Donald Trump said on Saturday that U.S. troops will start withdrawing “today” — but noted that he gave Gen. Scott Miller, commander of U.S. forces in Afghanistan, the authority to begin “at his pace.”

“This is going to be a long, windy, bumpy road, there will be ups and downs and we will stop and start, that’s gonna be the nature of this over the next days, weeks and months,” Esper said. “So I’m not going to get too excited about what happens in the moment.”

The deal, which would result in all U.S. troops withdrawing from the country in 14 months, is facing some pushback on the homefront from one of President Donald Trump's closest allies.

"Let's don't do in Afghanistan what Obama did in Iraq: pull the plug on the place and allow radical Islam to come roaring back," Sen. Lindsey Graham (R-S.C.) said Monday on "Fox & Friends". "We got a chance to end this Afghanistan war smartly and well but we're gonna need a residual U.S. force, a counterterrorism presence for years to come because I don't trust the Taliban to police al Qaeda and ISIS."

Rep. Mac Thornberry, the top Republican on the House Armed Services Committee, said he too has worries about the deal.

"t is not clear to me what the conditions are that would lead to our complete withdrawal in 14 months," he said at the Brookings Institution. "Who decides whether those conditions have been met, what the metrics are and so forth?”

On the most recent attacks, Afghan ambassador to the U.S. Roya Rahmani, who has just returned from Kabul, pointed to Esper’s comments in Kabul on Saturday promising a U.S. response if the Taliban do not abide by their commitments to maintain the reduction in violence.

“I have been told that the U.S. forces are ready, that if there is a violation they have full preparedness to react to that, “ Rahmani said at the embassy in Washington on Monday. “If Taliban want peace they should stop killing Afghans,” Rahmani said.

Rahmani noted that the one-week reduction in violence, which Esper said on Saturday marked the lowest level in years, has given the Afghan people “a glimmer of hope” for an enduring peace. But at the same time, officials in Kabul are concerned about the continued differences between the Taliban and Afghan government on key issues such as protecting women’s rights and other democratic values.

“We are hoping that we will arrive to a political settlement, that instead of meeting on the battlefield we will see them in a political arena,” she said.

Connor O'Brien contributed to this report.