Asif said Pakistan expects the fence to be completed by the end of 2019. USA officials said the freeze could affect $2 billion worth of assistance.
They said on Friday they have also been picking up terrorists' chatter through phone intercepts in which they were talking about Sajna's killing.
Pakistan has been under rising pressure to act against the Afghan Taleban and affiliated Haqqani network after US President Donald Trump accused officials in Islamabad of allowing them safe haven.
Relations between Washington and Islamabad have frayed in recent months after US President Trump's angry tweet on January 1 about Pakistan's "lies and deceit" over its alleged support for the Afghan Taliban and their allies.
Pakistan opposes USA drone strikes, saying they violate its sovereignty.
It's a free for all.
Asif said the roughly 600,000 Afghan refugees that went back to their home country past year have largely returned to Pakistan.More news: Black Panther Gets Second Rotten Review
Terming the camps breeding grounds for insurgency, the foreign minister said the global fraternity must do more to assist Pakistan with shouldering the burden of repatriation.
Pakistan has faced repeated criticism for the forced return of some refugees who have fled war across the border, which the United Nations says is against worldwide law.
The Trump administration imposed sanctions Wednesday on three individuals linked to Pakistan-based militant networks as it pushes Islamabad to crack down on perpetrators of attacks on Afghanistan.
North Waziristan and Paktika province in Afghanistan are adjacent to the border, and the officials and the terrorist commanders may have been reporting the same strike as two separate ones.
"Any free movement from their side to our side, or our side to their side, can breed mistrust and obviously some terrorist activity on our side or on their soil", Asif said.
The foreign minister said fencing the border is in the mutual interest of both Afghanistan and Pakistan. "We are targeting operatives who have provided logistical support, improvised explosive devices (IEDs) and other technological assistance to Al-Qaeda, Lashkar-e Taiba, Taliban and other terrorist groups", Treasury Under Secretary for Terrorism and Financial Intelligence Sigal Mandelker said.