The leader of the march, Vanessa Rae, describes herself as a descendent of one of Richard's close relatives. She led a group that consisted mostly of Yorkshire residents, The (York) Press reported.
Richard's body was recently unearthed from a parking lot in Leicester and was identified through DNA comparison with a descendant of his sister. The lot occupies the site of the church where he was buried after he was killed in the Battle of Bosworth Field in 1485.
"I think he should come back to York because he was loved here," said Sandra Wadley, a member of the Friends of Richard III. "He has no connection with Leicester apart from that he died nearby. It's not a case of finders keepers."
The Friends and the Plantagenet Association, a group with ancestral ties to Richard's family, are pushing for York. The Richard III Society, the best-known of the king's supporters groups, has been willing to go with Leicester.
But the society is upset with a decision by Leicester Cathedral to mark the king's new resting spot with a slab instead of a tomb, This is Leicestershire reports.
"Richard III was the last of the Plantagenet line which ruled England for over three hundred years," Phil Stone, the society's president, said. "It is only fitting that he be honored with a table tomb."
The government has left the decision in the hands of the University of Leicester, which excavated Richard's burial place. The royal family, descended from Richard's niece, Queen Elizabeth, the wife of Henry VII, have taken no public position on the issue.