A spokesman for Afghanistan's Taliban said the militia would cease attacks on UN Peace Day on Sunday and would not obstruct a three-day polio vaccination starting the same day.
The Afghan army and international military forces have also announced, after a call from President Hamid Karzai, that they would halt offensives on Peace Day, September 21.
"In respect for the international Peace Day, Taliban have issued a declaration that we are in a defensive position and we will cease attacks," a spokesman for the group, Yousuf Ahmadi, told AFP.
"If NATO and America and their followers respect this day for real, and avoid tricks and announce the ceasefire from the depth of their heart, the (Taliban) will also instruct to its own mujahedeen (holy warriors) to take the defensive position on this day," the statement said.
Ahmadi also said Taliban would "cooperate" with a three-day UN polio vaccination campaign due to start in volatile parts of the country on Sunday.
Vaccinators must however "keep in contact" with Taliban in areas they visit to make sure they were safe, he said.
Two Afghan doctors working on the polio campaign were killed in a Taliban suicide car bombing in the southern province of Kandahar a week ago.
The bomber attacked two marked United Nations vehicles as they travelled through a market, also wounding several civilians.
Ahmadi claimed the target of the bomb had been UN vehicles transporting "American soldiers."
The Taliban says its fighters are trying to free the country from Western "invaders." The militia's attacks kill more civilians than troops, also targeting school teachers, health workers and aid workers.
Afghanistan is one of a handful of countries that still has the crippling polio virus, with 18 new cases reported this year, all in the south and east where insurgent violence is the strongest and health workers most at risk.
Vaccinators have been unable to reach about 100,000 children in the south because of the insecurity, the World Health Organisation says.
The three-day campaign starting on Sunday is expected to reach 1.8 million children in six provinces in the south.
The United Nations confirmed it had received a letter from the Taliban about the Peace Day polio campaign.
"All statements of support for Peace Day are very welcome," spokesman Adrian Edwards told AFP.
"It's an apolitical campaign for peace and our objective in this is simple -- we want to open humanitarian space for initiatives such as polio vaccination.
"And on the political side, we want to open space to have peace back on the agenda."
The Taliban were in government between 1996 and 2001, when they were removed in a US-led invasion for sheltering Al-Qaeda after the September 11 attacks on the United States.
Their fight against the elected Afghan government and its allies has claimed thousands of lives.
In a new attack, a coalition soldier and two Afghans were killed Saturday when a bombing, similar to those used by insurgents, struck their vehicle in southern Afghanistan.