Virginia Gov. Charles S. Robb, facing the first personnel crisis of his 16-month-old administration, announced yesterday that the state's prisons director had resigned after refusing to propose cuts in his department's $485 million biennial budget.

The resignation of Raymond Procunier, known as a fiesty and blunt-talking administrator, climaxes a feud between the corrections chief and Robb's secretary of public safety, Frank White, that escalated rapidly this week.

After one heated meeting Wednesday, Procunier told reporters that White had "fired me," although gubernatorial aides quickly announced that only Robb had the authority to take such action.

Procunier, 59, a former head of California's prison system under Ronald Reagan, had been appointed to his $50,000-a-year post 13 months ago after Robb had mounted a nationwide search for the "best man for the job."

But confronted yesterday morning with a dispute between the agency director and White, one of six Robb cabinet secretaries and his highest ranking black administrator, Robb said there could never any doubt as to whom he would back. "It's very clear there's only one chief executive of the commonwealth," Robb said.

"We came to a situation where the differences that existed became so difficult to reconcile that it was in the best interest of Ray Procunier and the state we proceeded in this particular manner," the governor said.

White, a former member of President Carter's domestic policy staff from Silver Spring, said later that Robert Landon, now the state's deputy prison director for adult services, temporarily will replace Procunier.

The Associated Press last night reported Procunier is one of five out-of-state finalists for the job of corrections commissioner in Maryland, which is now vacant.

The controversy surrounding Procunier had been building for some time. Robb, who has warned agency heads repeatedly about a worsening fiscal problems, recently called on them to prepare proposals for "level funding" during the upcoming 1984-86 biennium.

Robb wanted each agency's budget to remain the same for the next two years as it has been for the past two years, without allowance for cost-of-living increases.

White, who oversees the corrections department, last week ordered Procunier to come up with specific budget recommendations from each of the state's prison wardens and have them on his desk this week. Procunier adamantly refused, an action that a member of the state board of corrections said infuriated White.

"You have two big egos there," said Claudette B. McDaniel, a Richmond City Council member who serves on the corrections board. "They're not on the same wave length . . . in terms of philosophy they see eye-to-eye on everything. But the personality clash was still there."

State Sen. Daniel W. Bird Jr. (D-Wythe), a member of the General Assembly's Joint Committee on Corrections, said Procunier had been directed to propose cuts totaling $26 million for the next two years.

In one state facility, Bland Correctional Center, that would have meant abolishing 15 positions on top of the 10 that were eliminated during Robb's last round of budget cuts, Bird said.

"The governor is trying to transfer funds from corrections into education and economic development, which are his priorities," Bird said. "But Procunier is a strong-willed individual, and he just rebelled."

Robb said at his news conference that the spending dispute was only the latest in a history of flare-ups in which Procunier threatened to quit if he was forced to take certain steps ordered by White.

"They had come close to the same situation four or five times in the past," Robb said. "The director felt there were certain circumstances he couldn't abide by and if he were requested to do something he would resign."

After Wednesday's alleged "firing," Robb attempted to mend the breach at an Executive Mansion meeting yesterday morning with Procunier, White and top gubernatorial aide David McCloud.

"It was my hope . . . that the differences could be resolved," Robb said. "But after listening to those most involved . . . it was clear to me and it was clear to the secretary of pubic safety that it was impossible to put the kind of working relationship back together we need to make this budget process go forward."

Procunier becomes the first Robb appointee to depart since the Democratic governor took office in January 1982. Having begun his career as a prison guard in California, Procunier worked his way up to become director of the state's prison system under Reagan in 1967. He later served as chairman of the California Parole Board under former Democratic Gov. Jerry Brown and then as chief of the Utah prison system.

Robb praised Procunier as a "real trooper" and said he was sorry to see him leave.

But, he added, "I cannot let my personal feelings toward him or the fine job he's doing in the corrections department to keep me from making judgments about that relationship. . . . It's a situation that transcends those considerations."