President Obama offered a plan Friday to reduce the costs of higher education by increasing the amount of federal grant money available for low-interest loans and tying it directly to colleges’ ability to reduce tuition.

In an impassioned speech before 4,000 students at the University of Michigan, Obama delivered an election-year pitch to the type of youthful audience that buoyed his 2008 campaign, saying his administration was putting colleges “on notice” that they must rein in soaring prices.

“You can’t assume you’ll just jack up tuition every single year,” Obama said to cheers at Glick Field House, the school’s indoor football facility. “If you can’t stop tuition going up, your funding from taxpayers will go down. We should push colleges to do better; we should hold them accountable if they don’t.”

Obama’s proposal would boost federal investment in the Perkins loan program from $1 billion to $8 billion and revamp the formula for distributing the money. Under the plan, colleges would be rewarded based on their success in offering relatively lower tuition prices, providing value and serving low-income students, the White House said.

The administration also is proposing to provide $1 billion in aid to states that curb higher education costs and to create a competition that provides $55 million in start-up funding for higher education institutions to pursue innovation to boost productivity.

However, most of the plan would require congressional approval, and Republicans have objected to adding expensive new proposals at a time of spiraling national debt.

White House officials said the Perkins loan portion of the president’s plan would not cost taxpayers additional dollars because students pay off the aid money with interest.

Obama’s appearance in Ann Arbor was the final stop of a three-day tour of five battleground states that aimed to build public support for the goal laid out in his State of the Union address this week: building an economy that offers more equity and opportunity for the middle class.

That message will frame the president’s reelection argument, and his focus on taming higher education costs echoes one of the central concerns of the Occupy Wall Street protests over the past year. Last fall, Obama announced a strategy to consolidate federal student loans and reduce interest rates to help college graduates pay off their debt.

In his remarks, Obama said access to higher education was a critical tool for young people eager to “do well enough to raise a family, own a home, send your own kids to college.”

“That’s what you’re striving for, what the American dream is all about,” he said. “How we keep that issue alive is the defining issue of our time. We do not want to be in a country that looks to success for only a small group of people. We want to be a country where everybody has a chance.”

Higher education leaders praised the bulk of the president’s proposals.

Obama also called on Congress to turn back a proposed doubling of the 3.4 percent interest rate on federal Stafford loans. And he is seeking to create a “College Scorecard” for every institution that is designed to present information about cost, graduation rates and future earnings in an “easy-to-read” format. The federal government has already taken steps in this direction with its College Navigator Web site.

Analysts said Obama’s plan probably would not affect the flow of federal Pell grants, the largest source of federal college aid, intended for low-income students.

But there is one potential drawback to the president’s plan: Punishing some colleges by denying them federal aid would affect needy students if those schools are unable to reduce costs.

“Do you take money away from low- and middle-income students and families because you are unhappy with the institution?” said Terry Hartle, senior vice president of the American Council on Education.

In inflation-adjusted dollars, average sticker price at private nonprofit colleges has doubled to $28,500 since the late 1980s, according to the College Board. But the “net” price of college, after factoring in student aid, has risen at a much slower pace and is essentially flat over the past five years.

Higher education officials question how the administration would determine whether a college is holding the line on tuition fees.

Colleges might be asked to limit net tuition increases to, say, 3 percent a year to avoid losing aid. But, the educators asked, would the president punish a public college that raised tuition to compensate for lost state subsidies? What if a college with historically low tuition approved a steep increase to avoid operating at a loss?

“That starts to get pretty sticky when you start to think of actual metrics,” said Haley Chitty, spokesman for the National Association of Student Financial Aid Administrators.

De Vise reported from Washington.