More than 800,000 borrowers will have $39 billion in federal student loan debt eliminated under a government effort to remedy years of mistakes by the loan servicers that collect payments on the government’s behalf.

Millions more people will have their loans adjusted as part of the programme.

The relief will go to those with federal loans owned directly by the education department and who enrolled in income-driven repayment plans. Those plans cap the payments that borrowers owe to a percentage of their income. Under those plans, borrowers must make payments for a term that is typically 20 or 25 years. Any remaining balance is forgiven.

More than eight million people use income-driven repayment plans, but for decades, many of the companies that bill borrowers made extensive mistakes in tracking payments and in guiding borrowers through the payment process. Those errors put millions of borrowers further behind by years in their quest to pay off their loans.

“For far too long, borrowers fell through the cracks of a broken system,” Miguel Cardona, the education secretary, said on Friday.

The planned move comes two weeks after the Supreme Court struck down President Joe Biden’s plan to eliminate $400 billion in student loan debt for tens of millions of borrowers. The court ruled that the President lacked the authority to eliminate debts so broadly without explicitly congressional authorization.

But the far smaller adjustment on Friday, which is separate and has not led to court challenges, falls more squarely within the education secretary’s power to administer loan repayment programs.

The debt elimination — which will happen in the next few weeks, the education department said — is part of a plan the Biden administration announced last year to address the problem of servicers’ mistakes.

The department decided to automatically and retroactively credit millions of borrowers for late or partial payments and for long stretches of time before the pandemic with their payments in forbearance.

The 804,000 borrowers whose debts will be eliminated are those who, after the adjustments, have made the required 240 or 300 monthly payments (depending on their payment plan) to have their remaining debt forgiven.

So-called “forbearance steering” was a particularly glaring issue, the department said last year. Low-income borrowers can qualify for monthly bills of $0 through income-driven payment plans, but loan servicers often placed struggling borrowers on forbearance — a move that kept their loans in good standing but meant that interest continued accruing, inflating borrowers’ balances.

The Consumer Financial Protection Bureau in 2017 sued Navient, which was then one of the government’s largest student loan servicers.