Hundreds of Dalit protesters gathered outside the hospital to support the family.
Vankar had immolated himself outside the Patan Collectors office on Thursday and had died of burn injuries at a private hospital in Ahmedabad the next day.
Dalit leader and Independent MLA Jignesh Mevani and Leader of the Opposition Paresh Dhanani met Vankar's kin at the Gandhinagar civil hospital. Vankar was part of Mevani's Rashtriya Dalit Adhikar Manch.
Protesters at the site turned away Karshan Solanki, the BJP MLA from Kadi, when he arrived at the hospital.
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"We will decide what to do tomorrow if the government does not accept our demands in writing," Mevani said.
He demanded the constitution of a Special Investigation Team (SIT), with a member from the Dalit community, to investigate Vankar's death and act against those responsible.
Vankar was fighting for Hemaben Vankar, a landless Dalit farm labourer, who had alleged that authorities were not allotting a plot of land to her family despite collecting Rs 22,236 in 2013.
In a memorandum submitted to the Collector a week ago, Hemaben, along with Vankar, had threatened self-immolation.
Gandhinagar Superintendent of Police Virendra Singh Yadav said around 250-300 protesters gathered on the premises of Gandhinagar civil hospital to support Vankar's kin, who refused to claim his body.
"They have been protesting peacefully and are meeting officials over their demands," he said.
The state government had ordered an inquiry into the incident to be helmed by chief secretary JN Singh.
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