Eleven major education groups yesterday urged President Carter to reject extensive budget cuts in student financial aid reportedly recommended by the Office of Management and Budget.

The organizations' leaders sent a letter to the president charging that letter to the president charging that the OMB proposals "violate both the letter and the spirit" of his administration's commitment to student aid. Carter last month signed a bill raising from $15,000 to $25,000 the income ceiling for families to be eligible for federally backed student aid.

OMB has proposed nearly halving the $3 billion that the Department of Health, Education and Welfare estimates is necessary to implement that law, known as the Middle-Income Student Assistance Act, the education groups, led by the American Council on Education, say.

OMB proposed cuts in three kinds of federal aid to education: Basic grants of up to $1,600 a year awarded solely on need; supplemental educational opportunity grants (SEOG) from $200 to $1,500 a year that must be matched by the school, and low-interest national direct student loans (NDSL) up to $5,000 per student at 3 percent interest, with up to 10 years beyond graduation to repay.

OMB has proposed cutting basic grant funds from $2.9 billion to $1.6 billion for fiscal year 1980, the SEOG from $370 million authorized by Congress to $270 million and eliminating the $286 million annual NDSL capital fund after fiscal 1980.

The $370 million for SEOG was "explicitly" required by Congress for the benefit of students in more costly colleges who need aid beyong the basic grants, the letter to Carter said. About 182,000 additional students would be helped by the higher amount.

Elimination of the capital funding for the NDSL program would "seriously restrict" the chances of going to college for many students who cannot get loans from private lenders , the groups told the president.

"There are students, sophomores and juniors, already in the system, who will not be able to continue their education" if the cuts are implemented, ACE President Jack W. Peltason said.

OMB and White House spokesmen would not comment on the reported proposed reductions and the groups' protest letter yesterday. They said the budget process is incomplete and the proposed cuts have not been officially aired.