The nation’s largest veterans groups are urging President-elect Donald J. Trump to keep President Obama’s secretary of veterans affairs, Robert A. McDonald, out of concern that his rumored candidates’ inexperience and ideological leanings could cripple the massive veterans health care system.

On the campaign trail, Mr. Trump was relentless in his criticism of the Department of Veterans Affairs, calling it “the most corrupt agency in the United States.” Some of the candidates mentioned to head the department have called for sweeping changes to make it easier to fire federal workers and privatize veterans’ health care.

But the major veterans groups, which together represent hundreds of thousands of veterans, said they favor the incremental reform they have seen under Mr. McDonald. On Friday, leaders of the American Legion, Disabled American Veterans, Veterans of Foreign Wars, Vietnam Veterans of America and Amvets told members of Mr. Trump’s transition team that they would not support other candidates that have been mentioned.

“We all want McDonald,” said Joe Chenelly, the executive director of Amvets. “He has a good business mind, he is experienced and we feel we can trust him.”