The Navy has just launched a recruiting drive touting the "New GI Bill" -- the package of education benefits for servicemen that President Reagan has asked Congress to kill.

"The services have been disloyal on this one," said a White House official, admitting the military has failed to fall in line on the bill.

A Navy spokesman confirmed his service has earmarked $3 million in its fiscal 1986 budget and $3 million in its fiscal 1987 budget to advertise the GI bill that Reagan wants off the books by Oct. 1 of this year.

The spokesman added that the Navy received the approval of top Pentagon officials to start the advertising campaign featuring the new GI Bill without mentioning in the ads that its benefits may be canceled by October.

Yet, according to White House officials, it was Defense Secretary Caspar W. Weinberger who recommended in internal budget debates that the administration go back to the less expensive Veterans Educational Assistance Program (VEAP), which preceded the new GI Bill, partly because the more generous provisions in the new bill were not needed to fill billets in the military services.

The White House notified Congress earlier this year that it would propose legislation to substitute VEAP for the current GI Bill, effective Oct. 1. Chairman G.V. (Sonny) Montgomery (D-Miss.) of the House Veterans Affairs Committee has vowed that such a bill will never get out of his committee.

Legislation to go back to VEAP could be approved in the Republican-controlled Senate, however, making the battleground a House-Senate conference.

The administration, in proposing the return to VEAP, told Congress that "the Department of Defense has determined that the new GI Bill is not necessary for recruitment and may be a disincentive for retention."

The General Accounting Office recently issued a report that said: "Army statistics show a marked recruiting improvement since the new GI Bill was started on July 1, 1985 . . . . The administration's position that a return to VEAP will provide sufficient recruiting incentives to meet manning requirements is not shared by military service program managers . . . . "

The Navy, undeterred by the administration's plan to sink the current GI Bill, is declaring in its ads that its Sea College Fund, together with the new GI Bill, will enable a high school graduate who serves on active duty for two years and in the reserves for six years to put away as much as $18,000.

A Pentagon spokesman said the Defense Department would have no comment on the seeming contradiction in the Navy's ad campaign and the administration's opposition to the GI Bill that it advertises.