According to the letter, the consulate will remain closed until adequate security arrangements were made.
In November, a Pakistani diplomat was shot dead outside his residence in Jalalabad. Last June, two Pakistani diplomats were kidnapped in Nangarhar while heading to Pakistan by road.
The closure of the consulate is the latest episode in a period of increasingly strained relations between the neighbouring countries who accuse each other of providing safe haven to armed fighters along the 2,600km, largely porous, border.
Pakistan has made efforts to fence the border, but has faced resistance from Afghanistan, who claims the border is disputed.
In August, Afghan President Ashraf Ghani accused Pakistan of supporting AfghanTaliban fighters who launched a five-day assault on the Afghan city of Ghazni.
Pakistani foreign office spokesperson Muhammad Faisal denied the charge, terming the complaint “spurious” and “rejecting [the] baseless allegations”.
Efforts have been under way since the election of a new government in Pakistan, led by Prime Minister Imran Khan, to reset the relationship.
In a congratulatory phone call to Khan after his election, Ghani said: “We both agreed to overcome the past and to lay a new foundation for a prosperous political, social and economic future of both countries Afghanistan and Pakistan”.
At a weekly press briefing on Thursday, Pakistani foreign office spokesperson Faisal reiterated that resolve.
“There is a need to move forward for betterment of our relations,” he said.
