Both clubs have proposals in the pipeline to build new grounds two junctions apart on the M62 motorway but the local authority last week insisted they would provide financial support for only one new stadium and called on the pair to put aside their differences and share it.
Wildcats chairman Ted Richardson told the club's supporters at half-time in today's (Sunday) Super League match against St Helens that Wakefield were committed to the stadium project being planned by the Wakefield and District Community Trust at Newmarket and had no intention of moving in with Castleford at their new Glasshoughton home.
"We are delighted to confirm that all parties are in agreement that Newmarket is the only stadium project that will carry the Wakefield name and that we will play in," said Richardson.
"We will remain steadfast in this goal."
Sir Rodney Walker, chairman of the stadium trust, said: "At a recent meeting involving Wakefield Council, the owner of the land at Newmarket, the Wakefield and District Community Trust and the Wildcats, an understanding was reached recognising that the Wildcats would concentrate their support for Newmarket and that a move to Glasshoughton was not an option.
"The meeting with Wakefield Metropolitan District Council agreed that all parties would work to that end."
Wakefield are thought to be considering a temporary ground-share at Barnsley's Oakwell Stadium in 2012 if their Super League licence is renewed next year.