Congress was “well within” its constitutional powers when it decided that the way to resolve a crisis in health-care costs and coverage was to mandate that Americans obtain insurance or pay a fine, the Obama administration told the Supreme Court on Friday.

The government filed its opening brief in the battle over the 2010 health-care overhaul, which has become the most controversial accomplishment of President Obama’s domestic agenda. Its resolution will define the court’s term.

Solicitor General Donald B. Verrilli Jr. told the court in his initial filing involving the “individual mandate” that the Constitution gives Congress vast powers to regulate economic activity and resolve a “crisis” in the national health-care market.

Lawmakers decided that requiring health insurance was the best solution “after years of careful consideration and after a vigorous national debate,” Verrilli told the court.

“That was a policy choice the Constitution entrusts the democratically accountable branches to make, and the court should respect it.”

The brief echoed the themes the administration has sounded in defending the Affordable Care Act through legal challenges throughout the country. But the new brief seemed to more fully embrace the argument that the act was also justified by Congress’s taxing powers.

Supporters of the legislation were more reluctant at the time it was passed to refer to the fines that would be levied on those who failed to obtain health insurance as a tax.

“That Congress used the word ‘penalty’ in the minimum coverage provision, rather than ‘tax’ is immaterial to whether it was a proper exercise of Congress’s power over taxation,” Verrilli wrote.

The court has scheduled 51 / 2 hours of oral arguments in the case over three days, March 26-28. Friday was the initial deadline for briefs on some aspects of the case. In separate filings, those challenging the law — the National Federation of Independent Business and Florida and 25 other states — argued that if the court struck the individual mandate, the entire law must fall.

The individual insurance requirement is the most controversial part of the law. Lower courts that have examined the issue have split on whether the Constitution gives Congress the power to require individuals to buy something they may not necessarily want.

A panel of the U.S. Court of Appeals for the 11th Circuit in Atlanta said that was too much, calling it a “wholly novel and potentially unbounded assertion of congressional authority.”

“We are unable to conceive of any product whose purchase Congress could not mandate under this line of argument,” wrote Chief Judge Joel Dubina and Circuit Judge Frank Hull.

But other appeals courts upheld the individual mandate as a political decision that was up to Congress and the executive branch, not subject to the second-guessing of the judicial branch. One appeals court said it was not the right time to decide the constitutionality of the mandate, which does not go into effect until 2014.

The three 11th Circuit cases accepted by the court are National Federation of Independent Business v. Sebelius; Florida, et al., v. Department of Health and Human Services; and Department of Health and Human Services v. Florida, et al.