Haley told reporters at United Nations headquarters, "They feel confident that the Taliban will be coming to the table".
The United States' decision to suspend security assistance to Pakistan will cast a shadow on the USA efforts to combat terrorism in Afghanistan, as Pakistan plays a pivotal role in the anti-terrorism campaign in the region, reported Radio Pakistan .
Pakistani officials privy of the development have confirmed to Dawn News that a delegation of the Taliban including Shababuddin Dilawar and Malawi Rasool, came from Qatar to explore prospects of resuming talks.
Nebenzia said he noted President Vladimir Putin's comment at his news conference in December "thanking the Americans for being in Afghanistan, for doing a job" and stressing the need for US-Russian cooperation on the issue. "And they said that as long as they're supporting terrorism in Pakistan the Afghan community is continuing to feel that it is not safe".
Coming back from a UN Security Council visit to Afghanistan, US Ambassador Nikki Haley underscored on Monday that the Kabul government wants world powers to raise pressure on Pakistan.
He said the government is trying to bring the Taliban to the negotiating table and on that issue the council thinks "it should be an Afghan-led, Afghan-owned process, and we as worldwide community can help them in achieving that goal".
The council visit followed the Trump administration's announcement this month that it was suspending military aid to Pakistan until it takes decisive action against militants.
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".
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.
Meanwhile, Taliban spokesman Zabihullah Mujahid said the Turkey meeting had no legitimate Taliban representatives in attendance.
The officials have also added that Islamabad has proposed to the Taliban delegation to hold direct talks with the Afghan government which has been turned down by the group.
Pakistan on Monday urged the U.S. to take their bilateral relationship forward during the first visit by a USA delegation since the suspension of security aid to the South Asian country over its perceived inaction against terror groups.