HOT SPRINGS, VA., OCT. 10 -- The newly appointed chairman of President Reagan's AIDS commission said today he hoped to move quickly to unite the dissension-torn panel, fill its vacancies, and prepare a preliminary report by a Dec. 7 deadline set when the commission was formed in July.

"My feeling is, we can do it. We haven't done the job to date, I'm sorry to say," James D. Watkins said at a news conference here after addressing a meeting of the Business Council, a group of top corporate executives. "I feel comfortable, and I think that the board, the members of the commission, feel comfortable that I can take it and mold them together to bring all our prima donnas, including me, into a nice, neat, unified package and move it."

"Can we make the Dec. 7 date? I'm the kind of person that, in my mind, says, 'Yes, we're going to do it,' " Watkins said. "I could almost write the report in my own mind conceptually right now: Mr. President, this is where we're going, this is what we've found, this is what we can do to contribute. We ask you to participate to this extent, we ask that the states move expeditiously on their laws."

Watkins, a retired admiral and member of the three-month-old committee, was named chairman by Reagan last Wednesday following the resignation of Chairman W. Eugene Mayberry, chief executive of the Mayo Clinic, and Vice Chairman Woodrow A. Myers Jr.

Mayberry and Myers said they stepped down because they were frustrated with infighting and ideological differences on the 13-member panel. The commission has been criticized by gay-rights activists and public health officials who charged that it does not have enough AIDS experts and has not lived up to its mandate to advise Reagan on the "medical, legal, ethical, social and economic impact" of acquired immune deficiency syndrome.

Watkins said he hoped to move quickly to fill the two vacancies on the commission, although he gave no details. He also said he had a candidate, whom he would not identify, to fill the post of executive director, which has been vacant for several weeks. He said he expected to name a new executive director for the commission by Tuesday.

Commission member William B. Walsh, who sources said had been a chief cause of frustration for Mayberry and Myers, appeared at the news conference with Watkins and indicated his support of the new chairman.

"Coming together with our commission next week for the first time under my leadership is going to require us to take a look at what we should have been looking at months ago, and we're going to do that really for the first time," Watkins said.