Dr Mohammad Shahid Baba's father Ghulam Qadir Baba said he did not know if his son had met militants during his trip to Karachi.
Raids are being conducted in Srinagar and Budgam district and several persons are being questioned after the police claimed to have foiled a terror plot in Srinagar with the arrest of a London-based Kashmiri doctor.
Dr Mohammad Shahid Baba, a physiotherapist, had planned to carry out attacks in Srinagar through Improvised Explosive Devices (IEDs), the police said.
He was arrested at Srinagar airport on Saturday, minutes before boarding a Delhi-bound flight. His three cousins -- a mechanical engineer, a PhD student and a government employee -- been arrested as well.
Police say a pistol was recovered from the arrested men, which Dr Shahid had received from some unidentified militant operative. But no explosives have been recovered from their possession.
Dr Shahid had visited Pakistan a year ago, where he was motivated to support militancy in Kashmir, the police said. He came to Kashmir two months ago, talked his cousins into joining his mission, and formed a sleeper cell.
The doctor's family -- who live in the Chadoora area of Budgam district -- says he was arrested while on way to London with his wife and 15-month-old daughter. He came to Kashmir with his family to attend a wedding, they said.
The doctor's father, Ghulam Qadir Baba, said his son was married to an US citizen of Pakistani origin and had visited Karachi after his wife gave birth to their daughter.
But he said he had no idea whether his son had met any militant leader during the visit.