William L. Ball III, the chief White House lobbyist, was selected yesterday by President Reagan to step into a simmering dispute over Pentagon budget cuts as the new secretary of the Navy.

The White House said the president will nominate Ball to succeed James H. Webb Jr., who resigned as Navy secretary Monday with a blast at Secretary of Defense Frank C. Carlucci.

"We look to Will Ball to continue working aggressively for a strong U.S. Navy," White House spokesman Marlin Fitzwater said, noting Webb's charge that Carlucci had needlessly sacrificed the administration's goal of a 600-ship fleet.

Fitzwater said the administration still seeks a 600-vessel Navy, but expects that the goal will be reached in fiscal year 1992, more than two years after Reagan leaves office, rather than in fiscal 1989 as originally planned.

"The budget restructuring under way at the Pentagon now is a difficult and painful process," Fitzwater said. "Secretary Carlucci is doing an admirable job. He's quite capable and suitable to the task, and he's carrying out the president's policies in that regard."

Ball, 39, who came to Washington as an aide to former senator Herman Talmadge (D-Ga.), has a reputation for skill at the behind-the-scenes compromises and maneuvers needed to steer legislation through Congress.

Ball has been assistant to the president for legislative affairs since February 1986. Before that he had been assistant secretary of state for legislative and intergovernmental affairs. From 1981 to 1985 he was administrative assistant to then-Sen. John G. Tower (R-Tex.), serving also as chief clerk of the Senate Armed Services Committee in 1981. He was Talmadge's administrative assistant in 1978.

A native of South Carolina, he is a graduate of the Georgia Institute of Technology and was a regular officer in the Navy from 1969 to 1975.

As secretary of the Navy, Ball will oversee about 584,000 Navy personnel and 199,000 Marines.

Ball's nomination requires confirmation by the Senate. He is expected to have little difficulty.