"They feel confident that the Taliban will be coming to the table", Ms Haley told reporters.
Ambassador Haley, who is also a member of President Trump's cabinet, said her takeaway from her visit is that "the entire peace process is Afghan-led and Afghan-owned".
The Taliban has exploited the instability to gain territory in Afghanistan after the end of NATO's combat mission in the country on January 1, 2015 and the withdrawal of foreign troops.
Pakistan is accused of supporting the Taliban and various militant groups in Afghanistan. They give safe haven to the terrorists we hunt in Afghanistan, with little help.
"They did ask us for consensus to put further pressure on Pakistan to come to the table and change their behavior", Haley said.
The tension between the United States and Pakistan has recently grown over USA complaints that the Afghan Taliban and Haqqani network that target American troops in Afghanistan are allowed to take shelter on Pakistani soil.
Ms Haley did not specify what measures could be taken to pressure Pakistan, but the council does have the power to impose sanctions. Islamabad denies this and accuses the United States of disrespecting its vast sacrifices in fighting terrorism.
Reuters reported that the Taliban's Haqqani network last week released 14 captured Afghan Army soldiers in the eastern province of Paktia as a goodwill gesture ahead of the talks.
Russian Federation called on Wednesday for urgent talks between the Afghan government and the Taliban, its Foreign Ministry said in a statement on Wednesday.
The Taliban group spokesman Zabiullah Mujahid had earlier rejected the participation of the group's representatives in the unofficial talks that took place in Turkey.