"The working groups are talking today. They begin their talks today. And the talks surrounds against the withdrawal of foreign troops from Afghanistan and also that the soil of Afghanistan should not be used against any other country."
"We have two core issues. The withdrawal of all foreign forces from Afghanistan is a core issue for us. And a core issue for the American side is that the soil of Afghanistan should not be used against the Americans and against its allies."
"When the occupation is ended there is full withdrawal of foreign troops from Afghanistan and there is an Afghan-inclusive Islamic government in the country. I think there is no need for any military operation in war. So there will be a sustainable peace in the country and all the military people and our people, they will be included in a national army."
"It is very important that the importance we give to these talks, that the Dipti Amir (chief) Mullah Baradar, he is here, present here. So that's how much importance we are giving to these talks and how much expectation that we have from these talks."
Taliban spokesperson Suhail Shaheen said in Doha on Tuesday that the withdrawal of foreign forces is a core issue in the talks aimed at ending the 17-year war in Afghanistan.
He said the talks concerned "the withdrawal of foreign troops from Afghanistan and also that the soil of Afghanistan should not be used against any other country."
He noted that the presence of the Mullah Abdul Ghani Baradar, a co-founder of the movement, showed the importance of these talks to the Taliban.
Baradar was released last year from a Pakistani jail where he had been held since his arrest in a joint Pakistani-CIA operation in 2010.
Baradar arrived on Sunday in Doha, the capital of Qatar, from Pakistan.
His presence in Doha, where the Taliban maintain a political office, and his lead role in the talks is considered significant because of his stature within the Taliban, who control or hold sway over nearly half of Afghanistan.
U.S. envoy Zalmay Khalilzad who met with Baradar is also expected to pressure the Taliban to hold direct talks with the Kabul government.
The closed-door discussions in Qatar, where the Taliban maintain a political office, are believed to be focused on a U.S. troop withdrawal from Afghanistan and on launching negotiations between the Taliban and the U.S.-backed government in Kabul.
Shaheen added that direct talks with the Afghan government would be "internal."
These talks were about "the external aspect and that's talking with the Americans about troops withdrawal from Afghanistan, and about their concern that no more Afghanistan be a security concern for them."