WASHINGTON — The Supreme Court rescued President Obama’s health care law on Thursday for the second time in three years, rejecting a conservative challenge to the law’s financial structure that could have proved fatal.

By a vote of 6-3, the justices ruled that federal subsidies can be offered in both state and federal health care exchanges, or marketplaces, putting the landmark 2010 statute on solid legal footing for the immediate future and handing the law’s opponents a sound defeat.

“Congress passed the Affordable Care Act to improve health insurance markets, not to destroy them,” Chief Justice John Roberts wrote for the court’s majority. “If at all possible, we must interpret the Act in a way that is consistent with the former, and avoids the latter.”

Roberts was joined by the court’s four more liberal justices, and by Justice Anthony Kennedy. The court’s three more conservative justices dissented.

The case turned on a section of the health law that said the federal government could subsidize health insurance for people who purchased it in a marketplace “established by the state.” That language, Roberts wrote, is “ambiguous” when read in context, and had to be read in a way that was consistent with the law’s overall goals. Limiting the subsidies to only state-run exchanges “could well push a State’s individual insurance market into a death spiral,” he wrote.

If Congress had meant to impose such a limit, “It would not have used such a winding path of connect-the-dots provisions,” he wrote.

Justice Antonin Scalia called the result “quite absurd,” and accused his colleagues of turning “somersaults” to re-interpret the health law to make it function. The result, he wrote, reveals “the discouraging truth that the Supreme Court of the United States favors some laws over others, and is prepared to do whatever it takes to uphold and assist its favorites.”

The high court’s action virtually guarantees that Obama will leave office in January 2017 with his signature domestic policy achievement in place. Republicans in Congress, who have tried more than 60 times to repeal the law or wipe out its funding, may be forced to throw in the towel.

The lawsuit was by far the most dangerous of several pending against what’s come to be called Obamacare. It threatened the tax credits used by 6.4 million people in 34 states to make health insurance premiums affordable.

Had it succeeded, proponents of the law warned, insurance markets in those states would have become unmanageable, with premiums rising and millions more uninsured. The White House, Congress and state officials would have been left scrambling to repair the law or create new state marketplaces.

The case from Virginia, King v. Burwell, represented the most serious threat to the health care law since the Supreme Court upheld it the first time in 2012. Chief Justice John Roberts wrote the court’s 5-4 decision then, upholding the law’s mandate that most people get insurance by equating its penalty with a tax.

This time, the dispute came down to four words in the 906-page statute that refer to tax credits offered in exchanges “established by the state.” Opponents, bankrolled by conservative interest groups, claimed that meant no tax credits could flow to states in which the federal government was running the marketplace.

Proponents said the phrase had to be taken in context with the entire law, intended to provide health coverage to “all Americans.”

When it was being crafted, lawmakers assumed most or all states would create their own exchanges. After it passed in March 2010, it became clear that many states led by Republican governors and legislatures would refuse, relying instead on the federal government to operate them.

In 2012, the Internal Revenue Service issued regulations making subsidies available in all states. The law’s challengers claimed that violated the letter of the law. They contended that lawmakers purposely made tax credits available only in state-run exchanges as an incentive for governors and legislatures to create their own marketplaces.

Proponents, backed by 22 states, argued that governors and legislatures never were told they needed to set up state exchanges in order for their citizens to get tax credits. The issue was not discussed when the law was being drafted and should not be considered now that millions of people would be harmed, they said.

The argument over subsidies in federal exchanges has been the focus of four separate cases. In King, the U.S. Court of Appeals for the 4th Circuit had unanimously upheld the law. Other cases pending in Washington, D.C., Indiana and Oklahoma now will be resolved based on the Supreme Court’s ruling.