The Pakistani government has given them until 31 May to shut their offices. These often double-up as residences for senior members, said a fighter belonging to one of the groups.
The move is seen as part of a gradual thawing in ties between Pakistan and neighbouring India.
"There is tremendous pressure from the Pakistani side to close our offices," said the leader of one group, who declined to be identified.
"There is complete unanimity in our ranks that we will not close down our offices-cum-residences in base camp," another fighter said, also on condition of anonymity.
Pakistani Kashmir separatist fighters call Pakistan-administered Kashmir the "base camp" for the separatist movement in Indian-administered Kashmir.
Until recently, Pakistan's crackdown on groups linked to Kashmir had been aimed mainly at the Pakistan-based Lashkar-e-Taiba and Jaish-e-Mohammad.
But it now appears to be concentrating more on Kashmir-based groups, including the largest, Hizb-ul-Mujahideen.
The decision to demand closure of the separatist groups’ headquarters follows the announcement of the resumption of diplomatic ties between India and Pakistan.
Relations between the two countries deteriorated after the 13 December 2001 attack on the Indian Parliament by alleged Kashmiri fighters.