GMB is fighting the company over its controversial Contract 6, which would remove workers' rights to take paid rest.
GMB state: "Asda was formed from a Leeds family company built on proud Yorkshire values of hard work and respect. They’d be spinning in their graves now."
But the employer has told its staff that they will find themselves jobless over Christmas if they do not sign the deal by November 02, sparking mass protests in Leeds and a 23,000-strong petition against the company.
The supermarket chain reported an increase in profits of over £92 million last year and its directors shared £12 million between them.
GMB has written an open letter to ASDA's Senior Vice President Hayley Tatum, asking that the firm stop threatening workers' livelihoods and sit down to negotiate a new deal instead.
Gary Carter, GMB National Officer, said: "If ASDA is serious about not wanting to sack thousands of its employees on the run-up to Christmas, they need to withdraw the dismissal notices and sit down with GMB to resolve this dispute.
"ASDA has served notice on up to 12,000 of its loyal employees – that cannot be right.
"The onus is now on them to save people's jobs with a better deal that their employees can sign up to."
Solidarity urges members to sign the petition to support Asda workers