Mullah Abdul Manan Niazi told a group of around 200 followers in eastern Afghanistan that his faction had no faith in the government but was willing to negotiate without preconditions.
Niazi is deputy to Mullah Mohammad Rasool, who split from the Taliban last summer after Mullah Akhtar Mansour was chosen to succeed the group's late founder, Mullah Mohammad Omar.
Mansour was killed earlier this month in a US drone strike in Pakistan and was replaced days later by a little known conservative, Mullah Haibatullah Akhundzada.
The main Taliban faction has expressed similar demands, but says it will only enter peace talks after they have been met. The US and NATO officially ended their combat mission more than a year ago, but thousands of foreign soldiers remain in the country, mainly carrying out training, support and counter-terrorism operations.
Mansour had refused to participate in a peace process initiated by Afghan President Ashraf Ghani that included Pakistan, the United States and China.
Representatives of the four countries have held five meetings, without inviting the Taliban. Their aim is to chart a road map toward talks between the Afghan government and the insurgents to end the 15-year war, but the disarray within the Taliban has complicated those efforts, the Associated press reported.
The Taliban's spokesman, Zabihullah Mujahid, has branded Rasooll’s faction "a government army in the shape of the Taliban." Speaking to the AP Sunday, he claimed that Rasool was supported by Kabul and Washington.
"For us he is nothing more than a local policeman or a puppet of Afghan intelligence," he said.
Rasool's followers met in the mountainous Shindand district, near the border with Iran. Snipers on hilltops surveyed dirt roads leading to the area, which serves as the main base for the mobile fighters. The encampment where the meeting was held is only accessible by motorbike or horse.
The turbaned followers of Rasool - who is believed to have been detained in Pakistan - appeared to be armed with new weapons, including automatic rifles and grenade launchers.
The Taliban have continued to launch major attacks on government forces despite the internal conflict, and the war has shown no sign of abating over the past year.
The Taliban attacked checkpoints in the southern Helmand province late Saturday, killing four police, according to the provincial governor's spokesman, Omar Zawaq.
Among those killed was local police commander Safar Mohammad, who in recent years had successfully kept highways in the area open to traffic. Zawaq said another nine police officers and one soldier were wounded in the attack.