Richard III's body becomes subject of rival claims from Leicester and York

In the corpse-strewn ending of Shakespeare's Richard III, the victorious Henry Tudor commands "Inter their bodies as becomes their births" – an order rapidly becoming tricky in the case of the most famous victim of the day's battle.

Rival claims to Richard's body have erupted within 24 hours of the formal confirmation that the remains excavated from a scruffy car park in the centre of Leicester are indeed those of the last Plantagenet king. Leicester has him, but York wants him.

So far Westminster Abbey, which holds both Richard's wife, Anne Neville, and Henry VII who defeated him, is maintaining a tactful silence, and nothing has been heard from Fotheringhay in Northamptonshire where he was born – but that may be just a matter of time.

As the face reconstructed from the skull was displayed – a faintly smiling man with a big nose and a notably determined jaw – Kersten England, chief executive of the City of York council, said it would be writing formally to the Department of Justice and the Crown "to invite their consideration of the views of the Duke of York's own people". Roughly translated, these views are: "Hand him over."

Leicester is equally determined to keep the man where he has lain since August 1485, when his body was brought back into the town naked and slung over the back of a horse – the traditional account newly confirmed by the revelation of the injuries to the skeleton. His body was claimed by the priests of Greyfriars church, and buried hastily but in a position of honour in the choir near the high altar.

The city's mayor, Sir Peter Soulsby, has already announced a new permanent visitor centre in an old school overlooking the site, planned to open next year on the same day as Richard's remains are reburied in the cathedral. A temporary exhibition in the Guildhall opens to the public on Friday.

However, York insists that burial there is what Richard himself would have wanted. "Richard III had – as now – very strong support in the city. His self-identification with the north and York is reflected in his plans for a chantry of 100 priests in York Minster where he wished to be buried,"England said. "That the burial site of this Yorkist king was determined by where he died from battle wounds makes the importance of adhering to his own wishes for his final resting place most important."

Both cities have started e-petitions for the right to bury Richard.

Leicester University says the terms of its exhumation licence, provide that the bones should be reburied close to the find spot. Conveniently, Leicester Cathedral is just 100 yards away.

The cathedral already has a handsome memorial stone to Richard, where visitors have left a constant supply of white roses since the story broke. Canon David Monteith said work had begun on an appropriate service for Richard, a multi-faith ceremony befitting one of the most racially diverse cities in England.