Education Secretary William J. Bennett, who consistently has defended Reagan administration efforts to cut deeply into federal education funding, is urging that the White House move away from its "budget-driven agenda" to defuse congressional criticism and promote administration initiatives more effectively.

At the same time, Bennett, acting on signals that the administration has agreed to relax its proposed budget ceilings, is preparing to submit a fiscal 1989 budget request significantly higher than his 1988 request, according to Education Department officials.

The officials said the proposed 1989 budget is likely to be $19 billion or more, compared to the $14 billion request for fiscal 1988, which begins Oct. 1.

The strategy represents a departure for Bennett, who has been criticized sharply on Capitol Hill for his proposed budget cuts in education. Congress has rejected not only the proposed cuts but most of Bennett's policy initiatives.

In memos this spring to White House chief of staff Howard H. Baker Jr., Bennett suggests that the administration continue to resist a tax increase but compromise on spending limits imposed by the Gramm-Rudman-Hollings balanced-budget law. The revised strategy would allow President Reagan to "more effectively take the offensive" and the Republican Party to establish itself as the party of "better ideas," Bennett argued.

Copies of the memos were obtained by The Washington Post. They suggested that, "after letting the Democrats take some deserved heat for breaking the Gramm-Rudman targets," the administration agree to stretch out the spending limits over the next few years. The argument reflects a recognition that substantial budget cuts in education would continue to be defeated in Congress.

"Unfortunately, no matter how good our ideas were, we tended to have little success in getting them across," said Bruce M. Carnes, deputy undersecretary of education. "The budget figures were quite an inviting target."

An official at the Office of Management and Budget said no official decision has been made on whether to relax spending limits for the fiscal 1989 budget, which will be released at the beginning of next year.

The news of Bennett's change of strategy drew mixed reaction.

One administration official, who asked not to be named, said the OMB budget targets for education continued to be far below the figures approved by Congress because Bennett, unlike most other agency heads, had not appealed the ceilings in the past.

"Bennett could have appealed that any year, and now he's choosing this year to paint himself as a hero," the official said.

"We'll believe it when we see it," said Charles Saunders, senior vice president for governmental relations at the American Council on Education, a higher-education organization. "Are we supposed to be jumping up and down because the department is proposing only a 10 percent cut instead of a 50 percent cut?"

OMB had set a $13.8 billion ceiling on education spending for fiscal 1989. A $19 billion budget request would still represent a reduction in the $20 billion to $21 billion budget Congress is expected to approve for 1988.

The Education Department's 1987 appropriation was $19.5 billion. In his 1988 budget request, Bennett proposed cuts of $5.5 billion, a third of overall budget cuts proposed by the administration.

According to one Education Department official, Bennett will funnel money in his 1989 budget into several programs he has espoused, including grants to encourage states to offer alternative certification programs for teachers and programs that allow parents more flexibility in choosing schools. In higher education, the department would continue to propose an expanded program for "income contingent loans," financial aid for college students in which repayment is based on income after graduation. The official said proposed student-aid cuts would be eased.