Outspoken Navy Secretary James H. Webb Jr. abruptly resigned yesterday, severely criticizing Defense Secretary Frank C. Carlucci's leadership ability and his demands that the Navy cut its budget.

Sources said William L. Ball III, the chief White House lobbyist, will be named today as Webb's replacement. Ball, who also has served as principal aide to former senators Herman Talmadge (D-Ga.) and John G. Tower (R-Tex.), is considered an effective and pragmatic White House liaison.

Webb, a staunch supporter of the Navy during his nearly 11 months as secretary, said Carlucci's insistence that the Navy remove 16 ships from the fleet -- indefinitely delaying its longtime goal of a 600-ship Navy -- was the catalyst for his resignation.

But, in a rare public airing of internal adminstration battles, Webb also said that he had become increasingly frustrated by what he perceived as Carlucci's indifference to his advice and Carlucci's lack of leadership in the Pentagon. {Related story on Page A21.}

"This building needs to be led," said Webb, 42, a decorated Vietnam war veteran and author of a best-selling novel about that war. "It needs leadership, it needs some vision. I'm saying that if I had a piece of advice to give to Secretary Carlucci, it would be to spend a lot more time with the top leaders in this building.

"He's been spending a lot of time with the State Department and a lot of time on the Hill," Webb told a small group of reporters summoned to his office yesterday. "I think they {Pentagon officials} need to feel his vision and to understand what he believes in."

In the resignation letter he sent President Reagan yesterday morning, Webb said he was "unable to support him {Carlucci} personally, or to defend this amended budget during budget deliberations."

Carlucci issued a two-paragraph response, saying he regretted Webb's resignation. A statement issued by the Defense Department said, "The {budget} compromises have not been easy for anyone and we regret the fact that the secretary of the Navy appears to have found himself unable to defend the department's decisions."

Reagan's expected nominee, Ball, was recruited for the White House by deputy chief of staff Kenneth M. Duberstein after serving as the lobbyist for the State Department. While at State, he won the plaudits of Secretary of State George P. Shultz, who once described him as a man "who talks slow and thinks fast."

No decision has made on a replacement for Ball, White House sources said.

Webb was appointed Navy secretary last April by then-Defense Secretary Caspar W. Weinberger. Some Pentagon officials said that relations between Webb and Carlucci, who succeeded Weinberger in November, have been strained.

Some Defense Department officials described Webb as "stubborn and uncompromising," with an unrealistic view of budget issues. Others characterized him as a courageous, outspoken defender of his goals for the Navy and Marine Corps, unwilling to support publicly administration policies that he did not support.

Webb was criticized sharply by administration officials for a recent speech in which he suggested that the United States should consider reorganizing military priorities throughout the world, including a possible withdrawal of some forces from Europe. That suggestion alarmed some NATO allies.

When Webb's office told a Norfolk newspaper that it was the defense secretary and not the Navy that had recommended cutting ships from the budget, Carlucci sent him a searing note saying he "assumed" Webb would deny the comments, according to Pentagon officials.

But the tension between the two increased dramatically during recent internal budget deliberations. Carlucci ordered military service chiefs to pare $33 billion from budgets to meet congressional deficit-cutting demands; the Navy's share was $12 billion.

Sources have said Carlucci's office criticized Webb's budgets for failing to make a serious effort at absorbing the Navy's share of the reductions.

Webb said he was repeatedly told that Carlucci wanted ships cut out of the budget, deflecting other options Webb suggested. That ended near-term chances of reaching a 600-ship Navy.

"Unfortunately, this is one of the few goals of the Reagan administration that was actually attainable," said Webb, who plans to return to writing.

Webb was also controversial within the Navy. He was praised by some officers for depoliticizing the officer selection system built by his predecessor, but was criticized by others as being too picky about details. He freqently chastised officers for wearing their uniform ribbons improperly.