Washington banks, which stopped making low-interest student loans almost two years ago, agree yesterday to resume making the loans June 1 after the federal and city governments promised to speed up repayment of about $4 million in defaults.

Officials of the D.C. Bankers Association said about $5 million for new loans would be available for city residence attending colleges and proprietary schools this fall. The loans would be completely guaranteed by the federal government.

Since 1967, nine D.C banks have made about $14.2 million in low-interest student loans that were guaranteed by the city government.

About 7,800 Washington residents received the money.

However, in June 1976 the banks stopped making new loans when the default rate topped 33 percent - about triple the average for all student borrowers nationwide - and the city government failed to honor its guaranty agreement even though it was eligible for an 80 percent federal reimbursement.

City officials said they did not have enough money to begin making repayments, and last July the banks sued to get it.

Yesterday, Leo Kornfeld, deputy U.S. education commissioner for student financial assistance, announced that the federal government would pay the banks directly for 80 per cent of the default loans.

City officials said the District now has $800,000 in a reserve fund to pay off the remainder.

According to Kornfeld, the banks will receive both federal and D.C. government repayments for 800 overdue loans within the next two months.

After that, he said they will receive repayment for 800 loans a month until all 3,800 notes now in default are paid. Kornfeld said the banks will have to show they compiled with federal regulations requiring them to make serious efforts to collect from defaulting students, but he said a preliminary check by his office indicated that in almost all cases this requirement had been met.

Harry W. Sipe, an officer of National Savings and Trust Co. who heads the policy committee of the bankers' association, said the banks would begin making new loans after they receive the first monthly repayment on defaults. He said he expects the banks to begin considering applications by June 1.

Late yesterday afternoon, lawyers for the bankers association, the city and the federal government announced in U.S. District Court here that they had reached an agreement on resuming the loan program and dropping the bankers lawsuit.

The lawyers said that a formal settlement had been drafted and that they expect it to be signed and filed in court within the next few days.

Kornfeld said the revived student loan program with direct federal guarantees will be broader that the program that had city government backing.

The old program had been restricted to students attending accredited two-year and four-year colleges and in post-graduate programs such as law and medicine.

The new program also will include students with high school diplomas who enroll in short vocational and technical programs and those operated by proprietary schools.

Last June, the federal government urged the local banks to take part in its direct loan guarantee program and offered to pay them 50 percent of what they were owed by the city. However, the bankers declared that they would make new students loans only when the old loans were paid.

Yesterday, Kornfeld said his office decided to offer a plan for full repayment within about six months because it as "absolutely essential that all students in the District be eligible to get loans again."

He said the District of Columbia was the only place in the country where low-cost students loan been suspended.

Since the student loan program started in 1965, about $11.1 billion in loans have been made to 6 million students throughout the nation.

About 40 percent of the money has come through the program of full federal guarantees, which will begin operating soon in Washington, while 60 percent has come through state guarantee agencies that now operate in 26 states.

Kornfeld said the default rate now is 12.5 percent in the direct federal program and an average of about 9 percent in the state-operated programs. He said no state has had a default rate of more than about 13 percent.

Wallace Gee, director of the city government's student loan office, said many of the 2,500 individuals who have defaulted on loans are college dropouts while another large group has completed graduate programs.

He said about 300 D.C. government employes, most of them teachers, are among the defaulters.

Under the new program, under-graduate students will be aligible to borrow as much as $2,500 a year to a maximum of $7,500. Graduate students may borrow as much as $5,000 a year to a maximum of $15,000.