The Taliban announced on Tuesday that they had come to an "initial agreement" to set up an overseas political office, possibly in Qatar, in their first public gesture towards peace talks with the US.
In a statement on their purported website "Voice of Jihad", the Islamists said they had held "preliminary talks with relevant sides including Qatar" to open an office outside Afghanistan, without confirming where it would be.
It is the first time the insurgent group has publicly raised the prospect of a negotiated peace after more than 10 years of fighting, always previously insisting they would not talk until all foreign troops had left Afghan soil.
One of their demands would be for a prisoner exchange to include the release of Taliban inmates from the US-run detention facility Guantanamo Bay, they said.
"We're now prepared, while having a strong presence inside (Afghanistan), to have a political office outside (Afghanistan) for negotiations," the statement said.
"And as part of this we have reached initial agreement with relevant sides including Qatar."
But the reported progress came as three explosions rocked the southern Afghan city of Kandahar on Tuesday, killing at least 12 and injuring 28 others, according to a police commander.
In the early evening, a suicide bomber detonated a tricycle in downtown Kandahar, killing four civilians and three policeman and injuring over a dozen, the police chief for the province General Abdul Raziq told AFP.
Earlier in the day, another suicide bomber set off an explosive-laden motorbike in the city centre, killing four children and one policeman, Raziq said. Sixteen others, including policemen and civilians, were injured.
The United States said Tuesday the Taliban, who claimed responsibility for the first explosion, must abandon violence before any real peace process can begin in Afghanistan.
"We welcome any step along the road... of the Afghan-led process towards reconciliation," White House spokesman Jay Carney said, while adding that the conditions for that so-called reconciliation "have not changed".
"We've always said that Taliban reconciliation would only come on the condition of breaking from Al-Qaeda, abandoning violence and abiding by the Afghan constitution, and that remains the case."
There are still about 130,000 US-led forces fighting the Taliban-led insurgency across Afghanistan, with coalition combat troops set to leave the country by the end of 2014, handing control for security to Afghan forces.
Signup to our newsletter and follow us on Facebook and Twitter!
But the US and its NATO allies have been pressing for political solutions to secure an end to the war.
The Taliban, now into an 11th year of fighting President Hamid Karzai's Western-backed government, called again for international troops to leave.
"The occupation of the country must be ended and Afghans must be allowed to create an Islamic government of their choice that be no harm to any one," they said.
The statement rejected some media reports that negotiations with the US had begun, but according to a source in Pakistan, early discussions were held last autumn in Doha, Qatar, between US diplomats and a small Taliban delegation led by Tayyeb Agha, the former secretary of Taliban leader Mullah Omar.
The source said Agha was the only Taliban official in direct contact with Mullah Omar, saying the Taliban's founder was based in Pakistan.
The comments come two days after Karzai publicly welcomed remarks by US Vice President Joe Biden that the Taliban "per se is not our enemy", saying they would help bring peace and stability to Afghanistan.
Biden's comments to Newsweek magazine triggered controversy in the United States but reflected an increasing focus on finding a political settlement as Western nations look to bring their troops home.
Karzai has agreed that if the United States wants to set up a Taliban address in Qatar to enable peace talks he will not stand in the way, as long as Afghanistan is involved in the process.
Separately, the Afghan president along with US embassy officials has met a delegation from Hezb-i-Islami, Afghanistan's second largest militant group led by former Afghan prime minister Gulbuddin Hekmatyar, officials said Tuesday.
A delegation representing the group travelled to Kabul and met the president on Sunday "in a good atmosphere, and the results were good", Karzai's spokesman Aimal Faizi told AFP, refusing to give further details.
The September assassination of Karzai's peace envoy, former president Burhanuddin Rabbani, had previously appeared to have derailed any prospects of progress in talks.
In the interview with Newsweek Biden emphasised the need for the Taliban to cut ties with Al-Qaeda.
As it pushes for a political settlement, the Afghan government has changed its tone towards the insurgents, referring to "terrorist" rather than "Taliban" attacks.
But many Afghans fear if the Taliban are allowed into mainstream politics, their influence will see the undermining of human rights and freedoms.