“Our leadership hasn’t conveyed any message about a ceasefire to us,” media outlets quoted the chief as saying on Monday, without mentioning his name.
Helmand and other southern provinces have seen bouts of fierce fighting in recent years.
Commanders in Paktika and Nangarhar, two other provinces located in the eastern part of Afghanistan and regarded as strongholds for the Taliban, were also of the same view, Presstv Reported.
Most recently, Taliban attacked Afghan government forces at a checkpoint in the northern province of Kunduz on Sunday night.
Taliban spokesperson Zabiullah Mujahid claimed in a statement that 19 security personnel had been killed.
The Afghan Defense Ministry confirmed the assault but put the death toll at five. It also said airstrikes were conducted in retaliation.
Also on Monday, Taliban said an Afghan military helicopter had been shot down in Nimroz province. But an official there said the aircraft had made an emergency landing and was not attacked.
Washington has for weeks been calling on the militants to hold attacks on US forces. US negotiators see this as a condition for resuming formal talks on an agreement that would see US troops leave the country after a near two-decade war.
Last week, US Secretary of Defense Mark Esper said the United States and the Taliban had negotiated a proposal for a seven-day reduction in violence, which could lead to an eventual withdrawal of US troops.
The two sides had been negotiating the deal for a year and were on the brink of an announcement in September 2019, when President Donald Trump abruptly declared the process “dead.”
Talks restarted in Qatar later in December last year, but were suspended again following an attack near the Bagram military base, which is run by the US.
Despite the violence on the ground, Mawlavi Abdul Salam Hanafi, deputy chief of the Taliban's Doha office, confirmed a deal with the United States is set to be signed by the end of February in a "signing ceremony" in the Qatari capital.
“Soon after signing the peace accord, the United States will release 5,000 of our prisoners and we will free 1,000 of theirs,” Hanafi said.
There are currently about 13,000 US troops in Afghanistan.