Refurbishment of the city's Mansion House has left councillor Sonja Crisp without an official residence.
In an email seen by the York Press she said: "A gentle reminder, I am the Lord Mayor, the first citizen, the rightful resident of the Mansion House."
In another email she said her mayoral chains were "in a disgusting state".
Due to the state of the chains, she said she was not going to wear them until she had confirmation they were to be re-gilded.
Chris Steward, the Conservative leader of the council, said he was "very disappointed" and it was "totally inappropriate behaviour for someone who has the honour of being Lord Mayor".
After stories about the leaked emails appeared in the national press Mrs Crisp, Labour councillor for Holgate Ward, told BBC Radio York the row had been "blown out of all proportion".
Her private emails complaining about her accommodation and mayoral chains were "stronger than they should have been" but "I'm not a prima donna", she said.
Her comments had been about the council's treatment of the office of mayor, she said.
A request for an alternative one-bedroom flat for changing clothes before official visits had been turned down by the council. "It was always implied to me alternative arrangements would be put in place," she said.
Mrs Crisp said the row was making her ill and she had collapsed twice. In an email she said the problems were "in no small part due to the stress and extra worry and work that my treatment by the council is causing me".
Mrs Crisp has confirmed she would continue as Lord Mayor of York.
The council is run by a coalition of Conservatives and Liberal Democrats.
The Lord Mayor of York has denied she is "a prima donna" after she sent email complaints about her accommodation and mayoral chains.