Budget Director Bert Lance won a warm reception today from Southern governors during a brief appearance at the closing session of their annual conference here.

Holding a walking press conference as he departed he said he has no intention of quitting his job and reported there had been no wavering in his support from President Carter.

In their dialogue with Lance, the governors appeared more interested in his efforts to balance the budget and curb federal "encroachment" into state affairs than in his personal financial problems.

They stood and applauded him when he was introduced and again when he completed his remarks.

Endorsing the administration goal of a balanced budget by 1981, Gov. James B. Hunt Jr. (D-N.C.) told Lance:

"I believe you are the person in the administration who is strongest in this. We stand ready to help you."

Gov. David L. Boren (D-Okla.) who today was elected vice chairman of the conference, also praised Lance.

"We feel that you have been a strong voice in the administration for strengthening the private sector and a strong voice in your remarks today toward bringing decisions back to the local level," Boren said.

In his remarks, Lance agreed with the governors that there have been "encroachments of federal government into affairs it has no business with" and that too many decisions affecting the state are delayed by red tape.

But he defended the administration's energy policy against charges at the conference that it will result in diminished production of oil and gas.

Lance told the governors that in developing an energy policy the President felt he would have to act on conservation "first and foremost."

He said that it was difficult to push conservation while at the same time creating incentives for production.

"We want to see more production," Lance said. "A good argument can be made that in the legislation and the plan there is ample encouragement of new energy sources.

On the economy, Lance said that President Carter's overriding concern was to bring about conditions "for steady growth without the ups and downs that lead to confusion and loss of confidence among the people.

"Many ordinary citizens . . . aren't sure of what's happening. They see indicators of where our economy is, and where it's going, bobbing like corks in a bathtub.

"Confusion breeds fear. Stability breeds confidence," Lance said in reiterating the government's "very firm . . . goal of balancing the budget in 1981.