"We have significantly increased the pace," added Esper.
The Trump administration suspended negotiations with the Taliban last month to end the 18-year conflict after Trump canceled a secret visit by Taliban negotiators to presidential retreat at Camp David in rural Maryland.
The meeting was expected to conclude a deal under negotiation since last fall, in which the US would reduce its troops in Afghanistan from the current 14,000 to 8,600, in return for the Taliban's commitment to open direct peace talks with the Afghan government and renounce international terrorist groups such as al Qaeda.
Esper declined to provide details of the intensified US operations, but said that they involve both aerial and ground attacks. He also emphasized that "Afghans carry out these operations on the ground", with US troops present in an advisory capacity.
Since the interruption of the talks, Trump has repeatedly claimed that US forces are hitting the Taliban harder.
For four days, we have hit our enemy harder than ever, and it will stay that way. Trump reiterated the claim the following week during a Pentagon ceremony marking the 18th anniversary of the September 11 attacks
However, the US military headquarters, which is responsible for operations in Afghanistan, has no new instructions from Trump to initiate further strikes and raids recognized.
Esper also said the Pentagon was still being considered to lower troop levels in Afghanistan.
"My goal would be to reduce troop levels to a level we know we can master and fulfill the core task," he said.
The Pentagon describes counter-terrorism operations against terrorist groups al-Qaida and the Afghan Islamic State's daughter as its core mission in the country. This is in contrast to the broader mission to help the Afghan government repel the Taliban uprising.
"If a commander is confident that he can reduce armed forces, I'll look at the right time to see if it's there, whether it's Africa, as you call it, to make sure I get to a more manageable level
Gen. Austin Miller, the supreme commander in Afghanistan, has already reduced troop levels from officially 14,000 to just under 13,000, POLITICO reported in August.