Dawud Aisha
Stanikzai, who until recently was the head of the Taliban's political office in Qatar and remains a leading figure in the group, was giving his first interview to the international media while attending a meeting in Moscow with senior Afghan opposition politicians earlier this month.
Stanikzai addressed the meeting in Moscow, saying the group did not want "a monopoly of power" - but that Afghanistan's constitution had been "imported from the West" and was an "obstacle to peace".
He said the Taliban's experiences in power in the 1990s, when it faced armed opposition from rival Afghan groups, had led the group to conclude it was preferable to reach a solution by "coming to the table".
"Peace is more difficult than war," Mr Stanikzai added, alluding to the difficulties in reaching a settlement. But he expressed hopes that the conflict could be brought to an end.
Mr Stanikzai has overseen a series of meetings with the US special envoy for Afghan reconciliation, Zalmay Khalilzad, in recent months.
In January, they reached what Mr Khalilzad termed as a "draft framework" of an agreement.
It was based on a commitment to withdraw US forces from the country, and a guarantee by the Taliban not to allow international jihadist groups to use Afghanistan as a base in the future.
Both sides have indicated that a number of issues still need to be resolved. However US President Donald Trump has made clear his desire to bring an end to the 17-year conflict and withdraw at least the vast bulk of American forces.
Stanikzai told the BBC he believed the Trump administration wanted to "bring peace to Afghanistan."
The meeting in Moscow is separate from the US-Taliban peace talks.
In addition to a Taliban delegation, it was also attended by former Afghan President Hamid Karzai, as well as other high-profile opposition figures.
Topics of discussions included how the country could be governed in the future, if the Taliban were to become a mainstream political force.
Early 1990s: The hardline Islamic movement emerges in northern Pakistan following Soviet withdrawal from Afghanistan.
1994: The predominantly Pashtun movement comes to prominence in Afghanistan, which is in the grip of civil war.
1996: Taliban seize control of Kabul and introduce the Islamic Republic of Afghanistan by making the Sharia law, it's state law.
2001: Taliban are toppled in US-led invasion of Afghanistan after 9/11 attacks in the US. The Taliban had sheltered al-Qaeda leader Osama Bin Laden, who was blamed for the attacks.
2014: Nato ends combat operations in Afghanistan. The Taliban, who retreated and regrouped after they were driven from power, are by now back with a vengeance.
The Taliban governed Afghanistan in 1996-2001 with the Islamic law. Mr Stanikzai said "women should not worry" about the prospect of increasing Taliban influence as they would seek to grant women all their "rights according to Islamic rule and Afghan culture".
"They can go to school, they can go to universities, they can work," he added.