The White House has agreed to give the Labor Department $2.4 billion for job training programs in fiscal 1983, a substantial boost over the $1.6 billion the Office of Management and Budget wanted to allow, sources said yesterday.

The decision preserves the bulk of the money the department had requested for its new business-labor training program (BLT), a private sector initiative the department hopes will replace the Comprehensive Employment and Training Act (CETA), which the Reagan administration wants to abolish.

The $2.4 billion total reportedly was approved by the president Wednesday night after an appeal by Secretary of Labor Raymond J. Donovan. Although the job training and public service employment program cost almost $8 billion in fiscal 1981, Donovan had requested $3.4 billion in fiscal 1983, and the OMB had cut that to $1.6 billion in its review.

The decision on the jobs programs is the first in a number of expected White House reversals of drastic cuts proposed by the OMB for most departments in its initial round of budget proposals for fiscal 1983.

Secretary of Housing and Urban Development Samuel R. Pierce Jr. and Secretary of Health and Human Services Richard S. Schweiker already have appealed deep slashes in housing and urban funds and in such programs as health research and services and Head Start.

The White House is expected to restore some but not all of the cuts. The job program decision, which split the difference between OMB and Labor, may set a pattern. The final figure for the job program in 1983, however, still would be far below that in both 1981 and 1982.

The $2.4 billion allowed for the job training programs includes $1.8 billion for the new business-labor training program, in which "consortia of private sector employers and organized labor" would provide training to targeted groups, such as minority youth, lacking job skills. Donovan had asked $2.2 billion for the new program, and the OMB had proposed $1 billion.

Under the White House decision another $400 million would be for the Job Corps, and $200 million for job and training programs for migrant workers, American Indians and the elderly.

However, the White House reportedly disallowed $321 million Donovan had requested initially for the work-incentive program, which provides training and placement for welfare clients, $200 million to wind down the remaining CETA training activities and $112 million for retraining of workers idled by entry of foreign products into the United States. The proposals also would phase out the summer youth job program, sources said.