Singh's sister Dalbir Kaur, who is fighting for his release from a Pakistani jail where he is languishing for the past over 20 years, and his daughter along with other relatives met External Affairs Minister S M Krishna who offered them help.
Before the meeting, the family sat on a dharna at Jantar Mantar.
Hours after reports emerged on Tuesday that Pakistan was to free Sarabjit, Presidential spokesman Faratullah Babar had said it was not Sarabjit but another Indian prisoner Surjeet Singh, who has been in jail for three decades.
Kaur said they cannot express in words the pain they have suffered. "The pain we have suffered I cannot express. I don't think this should have happened. After the cruel joke they have played, isn't it necessary for Pakistan to improve its image to release Sarabjit immediately," Kaur told reporters.
She said she is appealing to the Pakistan government to release Sarabjit for the sake of humanity.
Kaur said she was happy that the Indian government is taking all possible measures to get Sarabjit released.
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"I am assured that the issue of release of Sarabjit will be raised during the Indo-Pak meetings. I am feeling good that the government is showing concern and I trust them that they will support us. The Minister told me that we won't leave Sarabjit in Pakistan at any cost," she said.
On the release of Surjeet Singh, another prisoner who was released from Pakistani jail after languishing for 31 years, Kaur said she was happy for them.