President Carter asked Congress yesterday for a major expansion of federal aid to education and a restructuring of the program to provide more emphasis on the basic skills of reading, writing and arithmetic.

In proposing an increase in federal spending for elementary and secondary education from $6 billion to $6.9 billion, the president asked that $400 million, or almost half the increase, be earmaked for school districts with heavy concentrations of children from poor families.

Carter's other main proposals would:

Create a new incentive program under which the federal government would provide an additional $1 in aid for every $2 a state spent in a compensatory education program of its own. Twelve states, including Maryland, already have programs that would qualify under the proposal, according to administration officials.

Provide special federal assistance for demonstration projects in basic skills training and competency testing.

Tighten existing regulations to assure that poor children in nonpublic schools receive the federal aid to which they are entitled.

Increase assistance for bilingual education and to school districts that are developing or implimenting desegregation plans.

Revise the federal impact aid program to eliminate from the aid calculations children whose parents work for the federal government outside the country in which the child's school district is located.

In the Washington area> this proposed change would strike hardest at Fairfax County, where there are large numbers of children whose parents works at the Pentagon, in Arlington County.

Two years ago, the impact aid formula was revised to eliminate payments for children of federal employes who cross state lines to get to work. That eliminated from the aid calculations children whose parents work for federal agencies in Washington and live in the suburbs.

The president, flanked by Vice President Mondale and Health, Education and Welfare Secretary Joseph A. Califano Jr., unveiled the proposals at the White House, emphasings their concentration on basic skills.

"Today's proposals will focus our nation's resources on helping our children master the basic skills -- reading, writing and arithemetic -- which remain critical to their ability to function in a complex society," he said. "We must do a better job of teaching these basic skills to all our children."

Califano called the administration budget proposals "extraordinary" and "unprecedented."

"This is one of those moments in which I wish Lyndon Johnson were alive to see what President Carter has dome for that federal commitment that began 12 years ago," he said. Califano was an aide to Johnson when the Elementary and Secondary Education Act was enacted by Congress in 1965.

Carter asked for the largest spending increase in the program since 1966. Federal aid accounts for less than 10 per cent of the more than $80 billion a year spent for elementary and secondary education.

Rep. Carl D. Perkins (D-Ky.), whose subcommittee on elementary, secondary and vocational education act extension yesterday, predicted House passage of the administration proposals by May 1.

The National Education Association endorsed the legislation. John Ryor, NEA president, said Carter had made "the most comprehensive proposal for bringing education to the forefront of our priorities we've seen since the days of Lyndon Johnson."

Of the $6.9 billion in federal spending for education in the fiscal year that begins Oct. 1, almost $3.4 billion would be so-called Title I funds - money earmarked for children from poor families.

These funds, which currently aid 5.6 million children in 14,000 school districts, are divided among the states and local school districts on the basis of the number of children from poor families in each.

The president proposed no charge in the basic distribution formula, but he did ask that $400 million of the Title I funds go to school district in which the number of children from poor families is 5,000 or 2o per cent of total enrollment.

Califano estimated that under this formula two-thirds of the $400 million would to go big city school districts, 25 percent to rural school districts and about 7 percent to suburban school districts.

Testifying before Perkins' subcommittee yesterday, Califano arfued that an expansion of Title I aid - for which nonpublic school students are eligible - is preferable to congressional proposals for a tuition tax credit to ease the burden of private education.

The administration proposals contained no spending amounts for the special basic skills program or the incentive grants to states with compensatory education programs, neither of which would be effective until the fiscal year that begins Oct. 1, 1979.