Rankin travelled to the Puthukkudiyiruppu region of Mullaitivu on Tuesday, to speak directly to Tamil families about the problems they faced.
Following his visit intelligence officers arrived at the house and “threatened” the family, the Jaffna based newspaper, Uthayan, reports.
The family was one of three households visited by the High Commissioner during his trip.
The High Commissioner was told about a multitude of grievances faced by Tamils in the North-East, including poverty and obstacles to trade and livelihoods as well as the problems faced by Tamil women and young people, said the Northern Provincial Councillor Thurairasa Ravikaran.
On Monday, Mr Rankin visited a demining site in Muhamalai, where work is being carried out by UK based agency The Halo Trust.