WASHINGTON — The Supreme Court on Monday made it harder to prosecute public officials for corruption, unanimously vacating the conviction of Bob McDonnell, a former governor of Virginia.

Chief Justice John G. Roberts Jr., writing for the court, narrowed the definition of what sort of official act can serve as the basis of a corruption prosecution.

The act must be a formal, specific, and focused exercise of government power, he said, “such as a lawsuit, hearing, or administrative determination.’’ And prosecutors must prove, the chief justice continued, that the defendant made a decision or took action on the matter, or agreed to do so.

The alternative, Roberts wrote, would be to criminalize routine political courtesies. If corruption is defined too broadly, the chief justice wrote, government officials would be wary of serving their constituents.

The Supreme Court returned the case to an appeals court for an assessment of whether prosecutors in McDonnell’s case had presented evidence to satisfy the narrow definition of corruption announced Monday. If so, prosecutors may seek to retry McDonnell, but under the stricter standard.

In a statement, McDonnell said he was innocent and expected to be vindicated.

“I have not, and would not, betray the sacred trust the people of Virginia bestowed upon me during 22 years in elected office,’’ he said. “It is my hope that this matter will soon be over and that my family and I can begin to rebuild our lives.’’

McDonnell, a Republican, was charged with using his office to help Jonnie R. Williams Sr., who had provided the McDonnells with luxury products, loans, and vacations worth more than $175,000 when McDonnell was governor.

The gifts themselves were legal, and the question in the case was whether they were part of a corrupt bargain in which McDonnell reciprocated by using the power of his office to help Williams.

McDonnell arranged meetings for and attended events with his benefactor. But Williams, whose company made a diet supplement, did not have any real success in obtaining support for his product from the state. A jury found that McDonnell’s actions amounted to corruption, and a federal appeals court upheld the conviction.

In a separate ruling Monday, the Supreme Court upheld the broad reach of a federal law that bars people with misdemeanor domestic violence convictions from owning guns.

The justices rejected arguments that the law covers only intentional or knowing acts of abuse and not those committed recklessly — where a person is aware of the risk that an act will cause injury, but not certain it will. As examples, the court mentioned throwing a plate in the heat of an argument, or slamming a door.

The case involved two Maine men who said their guilty pleas for hitting their partners should not disqualify them from gun ownership.

Writing for herself and five other justices, Justice Elena Kagan said that Congress enacted the gun law some 20 years ago to close a loophole and ‘‘prohibit domestic abusers convicted under run-of-the-mill misdemeanor assault and battery laws from possessing guns.’’

She said if the law were read to exclude misdemeanors in which a person acted recklessly, it would ‘‘substantially undermine the provision’s design.’’

Gun-rights groups had argued that Stephen Voisine and William Armstrong III should not lose their constitutional right to bear arms, while advocates for victims of domestic abuse pushed to preserve the restriction.

The case isn’t among the more important ones of the term. White House spokesman Eric Schultz said although the Obama administration is pleased with the ruling, it wouldn’t have a significant impact on the debate in Congress about gun control, a debate renewed by a mass shooting earlier this month that left 49 people dead at a gay nightclub in Florida.

Although ruling in his favor, Roberts stopped well short of endorsing McDonnell’s actions.

“There is no doubt that this case is distasteful; it may be worse than that,’’ the chief justice wrote. “But our concern is not with tawdry tales of Ferraris, Rolexes, and ball gowns. It is instead with the broader legal implications of the government’s boundless interpretation of the federal bribery statute.’’