WASHINGTON — Along with the major health care legislation, the House on Sunday approved a major revamping of federal student loan programs that eliminates fees paid to private banks to act as intermediaries.

Instead, the government will expand a direct lending program, a step that the Congressional Budget Office said would save taxpayers $61 billion over 10 years, and use the money to increase Pell grants for students.

The student loan bill is a centerpiece of President Obama’s education agenda, and it was included in the budget reconciliation measure that also made final revisions to the Senate-passed health care bill.

The bill sets automatic annual increases in the maximum Pell grant, scheduled to rise to $5,975 by 2017 from $5,350 this year. The new Pell initiative also includes $13.5 billion to cover a shortfall caused by a steep rise in the number of Americans enrolling in college and seeking financial aid during the recession.