Members of the Leeds Minster Society of Change Ringers voted to turn down the invitation from York's Dean and Chapter. The vote saw 13 members of the group choosing to turn down the invite with two abstentions.
Speaking to York Post, deputy ringing master Robert Childs said the sound created by York's bells is the finest in the country but the group turned down the offer as a show of solidarity with York's 30 volunteer ringers who were dismissed in October.
A York Minster spokeswoman told the Post: "We can't comment for Leeds Minster or their bell ringers. It wouldn't be appropriate or courteous.
"One of our main ambitions is to make our Tower more accessible and welcoming to those who have already expressed an interest in volunteering for our bell tower and we also keen to respond to those who have expressed an interest in learning bell ringing in the future," she added.
More than 17,000 people have signed a petition calling for York's ringers to be reinstated after their sudden dismissal.
The Archbishop of York was forced to address the issue in October.
Dr John Sentamu said some individuals from the group had repeatedly undermined efforts by the landmark's governing body, the Chapter of York, to enforce safeguarding, security, health and safety rules. The society have denied Dr Sentamu's claims.