The Islamic State’s radio station released a statement on Saturday claiming that two of the group’s followers had carried out the shootings that left 14 people dead in San Bernardino, Calif., on Wednesday.

It was the first official claim of responsibility by the group after days of congratulatory messages posted on Twitter and a statement published on a news forum believed to be run by members of the Islamic State, which is also known as ISIS or ISIL.

In its English-language broadcast, the Islamic State’s Bayan radio station referred to the couple who carried out the attack as “soldiers of the caliphate,” a term denoting members of the terrorist group’s army.

The Islamic State group has used the same term to refer to gunmen who have carried out attacks in its name, including Elton Simpson and Nadir Soofi, who fired on a site hosting a Prophet Muhammad cartoon competition in Garland, Tex., in May.

A school security guard was wounded before a traffic police officer killed both gunmen.

A French gunman, Amedy Coulibaly, also referred to himself as a “soldier of the caliphate” in a video he recorded just before he attacked a kosher supermarket in a suburb of Paris in January.

In the broadcast about the California shootings, the Islamic State said, “Two soldiers of the khilafah executed an attack on the Inland Regional Center in San Bernardino on the 20th of Safar,” said a transcript provided by the SITE Intelligence Group, which tracks jihadist propaganda. Safar is the second month of the Islamic calendar.

“Light weapons were used which led to the deaths of 14 disbelievers,” the broadcast said.

But the Arabic-language broadcast differed from the group’s broadcast in English.

In the Arabic version, the assailants are referred to as “supporters” of the caliphate, a term denoting a less direct connection to the terrorist group.

It was unclear why the two versions differed.

Since the San Bernardino killings, law enforcement officials have confirmed that they are treating the episode as an act of terrorism.

One of the attackers, Tashfeen Malik, posted her “bayat,” or oath of allegiance to the Islamic State, on a Facebook page moments before the attack began.

The Islamic State has instructed those who wish to act in its name to publicly pledge allegiance to the group before carrying out any attack. Such a pledge has sometimes been the only visible link between the attacker and the terrorist group.

In the Texas attack, Mr. Simpson posted his oath on Twitter as he was driving to the site, and he asked his followers to follow Junaid Hussein, a well-known member of the Islamic State, who continued posting messages on Twitter after Mr. Simpson and Mr. Soofi were killed.

David Bowdich, the F.B.I. assistant director in charge of the Los Angeles office, said he was aware of the post by Ms. Malik, which was taken down by Facebook on Wednesday.

“There’s a number of pieces of evidence which has essentially pushed us off the cliff to say we are considering this an act of terrorism,” Mr. Bowdich said.

Earlier, Al Amaq, a news forum linked to the Islamic State and believed to be run by its members even though it is not an official publication of the group, issued a statement calling the couple “supporters” of the caliphate. The differences in the words used in the various broadcasts and statements cannot be immediately explained.

Investigators on Saturday were chasing down leads, examining the electronic media and other information seized from the couple’s home and going through it to compare it with evidence in other investigations. The authorities said they were especially concerned about possible copycat activity. “Thus far, we’re not seeing anything like that,” said a senior administration official who spoke on the condition of anonymity to discuss the investigation.

The authorities were examining what might have been the triggers for the killings. Among other things, they were trying to determine whether the wife had radicalized the husband or vice versa. But they remained perplexed by the couple’s turning to such a violent path after having had a baby just six months ago. “There’s a lot that doesn’t make sense,” the official said.

The accumulation of armaments, the evident planning that went into the attack, and the wife’s pledge to the Islamic State all pointed to radicalization. But no direct contact with known terrorist organizations had been unearthed as of Saturday afternoon.

Also Saturday, President François Hollande of France offered his condolences to President Obama in a telephone call, the White House said in a statement. Mr. Obama briefed Mr. Hollande on the investigation and the two leaders pledged to continue cooperating “to fight terrorism, both abroad and at home,” the statement said.