Haley joined the 14 other council envoys for talks with top Afghan leaders in Kabul at the weekend as the government considers holding peace talks with the Taliban to end decades of insurgency.
"They feel confident that the Taliban will be coming to the table," Haley told reporters at UN headquarters.
While the peace talks will be Afghan-led, the Kabul government did request that the Security Council weigh in to bring Pakistan onboard.
The Afghan government is making strides towards stability, she said, and "continue to make ten steps forward and with Pakistan they feel like they continue to take steps backward."
"As long as they are supporting terrorism in Pakistan, the Afghan community is continuing to feel it is not safe," she said.
Haley did not specify what measures could be taken to pressure Pakistan, but the council does have the power to impose sanctions.
Pakistan has long been accused of supporting the Taliban and various militant groups in Afghanistan -- charges it denies.
A question mark also hangs over a further USD 1 billion of US military equipment for Pakistan.
US officials believe that Pakistan's intelligence agency and military have long helped fund and arm the Taliban to counter rising Indian influence in Afghanistan, whose government is backed by the US.
The Afghan government also requested council help to address narcotics production and trafficking, looking at "every country that moves them," said Haley.
Kazakhstan's Ambassador Kairat Umarov, who led the council trip, said parliamentary elections must take place this year and be transparent "to ensure the credibility of the government" and "prevent further destabilization.
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