The statement from Massoud, head of the National Resistance Front of Afghanistan, came after Taliban forces said they had fought their way into the provincial capital of Panjshir Valley in Afghanistan's north.
The leader of the Afghan opposition group resisting Taliban forces in the Panjshir valley north of Kabul has said that he welcomed proposals from religious scholars for a negotiated settlement to end the fighting.
Ahmad Massoud, head of the National Resistance Front of Afghanistan (NRFA), made the announcement on the group's Facebook page.
Earlier, Taliban forces said they had fought their way into the provincial capital of Panjshir after securing the surrounding districts.
"The NRF in principle agree to solve the current problems and put an immediate end to the fighting and continue negotiations," Massoud said in the Facebook post.
"To reach a lasting peace, the NRF is ready to stop fighting on condition that Taliban also stop their attacks and military movements on Panjshir and Andarab," he said, referring to a district in the neighbouring province of Baghlan.
Earlier, Afghan media outlets reported that an Ulema council of religious scholars had called on the Taliban to accept a negotiated settlement to end the fighting in Panjshir.
Taliban advance deep into Panjshir
Taliban fighters advanced deep into the last holdout province of Panjshir Sunday, as the top US general warned Afghanistan faces a wider civil war that would offer fertile ground for a resurgence of terrorism.
Following their lightning-fast rout of Afghanistan's army last month – and celebrations when the last US troops flew out after 20 years of war on Monday – the Taliban are seeking to crush resistance forces defending the mountainous Panjshir Valley.
The Taliban, who rolled into Kabul three weeks ago at a speed that analysts say likely surprised even the hardline Islami sts themselves, are yet to finalise their new regime.
But top US General Mark Milley questioned whether they can consolidate power as they seek to shift from a guerrilla force to government.
"I think there's at least a very good probability of a broader civil war," said Milley, chairman of the Joint Chiefs of Staff, in a bleak assessment.
"That will then in turn lead to conditions that could, in fact, lead to a reconstitution of Al-Qaeda or a growth of ISIS (Islamic State group)," he told Fox News Saturday.
Taliban official Bilal Karimi on Sunday reported heavy clashes in Panjshir, and while resistance fighters insist they have the Taliban fighters at bay, analysts warned they are struggling.
The Italian aid agency Emergency said Taliban forces had reached the Panjshir village of Anabah, where they run a surgical centre.
"Many people have fled from local villages in recent days," Emergency said in a statement Saturday, adding it was continuing to provide medical services and treating a "small number of wounded".
Anabah lies some 25 kilometres (15 miles) north inside the 115-kilometre-long v alley, but unconfirmed reports suggested the Taliban had seized other areas too.
Bill Roggio, managing editor of the US-based Long War Journal, said Sunday that while there was still a "fog of war" – with unconfirmed reports the Taliban had captured multiple districts – "it looks bad".
Both sides claim to have inflicted heavy losses on the other.
"The Taliban army has been hardened with 20 years of war," Roggio tweeted Sunday, adding that "the odds were long" for the Panjshir resistance.
Roggio noted that the Taliban seized "a massive amount of weapons" after the US withdrawal and the collapse of the army.
The United States invaded Afghanistan and toppled the first Taliban regime in 2001 in the wake of the 9/11 attacks by Al-Qaeda, which had taken sanctuary in the country.
Washington has said it will maintain an "over-the-horizon" capability to strike against any threats to its security in Afghanistan.
The international community is coming to terms with having to deal with the new Taliban regime with a flurry of diplomacy.
US Secretary of State Antony Blinken is due Monday in Qatar, a key player in the Afghan saga and the location of the Taliban's political office, though he is not expected to meet with the militants.
He will then travel to Germany to lead a virtual 20-nation ministerial meeting on Afghanistan alongside German Foreign Minister Heiko Maas.
United Nations Secretary-General Antonio Guterres is also set to convene a high-level meeting on Afghanistan in Geneva on September 13, to focus on humanitarian assistance for the country.