Bob Parry, president of the Farmers' Union of Wales, walked out of the meeting in Cardiff saying it would be hypocritical for him to stay. Ms Gwyther, 36, has not eaten meat for 20 years. Mr Parry said: "My members will not be happy until she reconsiders her position. Somebody who does not eat meat cannot support the agriculture industry."
Ms Gwyther said she had not considered resigning. She said:"When Alun Michael [Welsh Assembly First Secretary] offered me that job he assured me I was the best person for the job and nothing since has changed my mind about that."
She said she was not a "naive vegetarian" and would do her utmost for farmers in Wales.
Other farmers' leadersstayed in the meeting and afterwards Mr Michael said most had expressed support for Ms Gwyther. He added: "I think Christine is the right person for the job."