LONDON—American and British counter-terror officers have turned their fire on the keyboard warriors waging jihad from their bedrooms in Western capitals.

A teenage boy from the D.C. area and a woman living in South London admitted Thursday in courtrooms 3,000 miles apart that they were “Twitter terrorists”—part of a growing online army that encourages Western citizens to travel to the so-called Islamic State; take up arms; or martyr themselves in the name of jihad.

Such is the perceived threat from these social media recruiting sergeants that judges on both sides of the Atlantic have dispensed with free speech arguments and now characterize Twitter or Instagram propaganda sites for al Qaeda and Islamic State (also known as ISIS and ISIL) as providing “material support” for terrorists.

Ali Shukri Amin, 17, of Manassas, Virginia, pleaded guilty to encouraging terrorism on Twitter and offering to teach would-be terror funders how to use Bitcoin to circumvent the authorities. He will be sentenced later in the summer. Alaa Abdullah Esayed, 22, of Kennington, London, admitted that she had posted 45,600 terror tweets on an account so ferocious that it was listed as one of al Qaeda’s top 66 jihadi accounts. She was sentenced to three years in prison.

Neither of them had any intension of putting their own safety at risk, but they called on thousands of online followers to do just that.

Esayed’s account had a profile picture of a woman in a full burqua holding an assault rifle. She urged mothers to train their children to become terrorists. In one post she wrote: “When the boy starts school, let him like Kalashnikov, raise him on following pictures of weapons, so that he likes them instead of clinging to the Play Station machine.”

She posted images of jihadi fighters who had died in battle and prisoners who were about to be executed. “Yes I am a terrorist, I appeal to every soul,” she wrote.

On the account @bentalislam, which means “Daughter of Islam” she tweeted an average of 58 posts a day. She had 8,534 followers but many more people would have seen her prolific output.

Judge Charles Wide, who sentenced Esayed at the Old Bailey in Central London, said it was vital that these Twitter terrorists be stopped. “This material and its dissemination is an important factor in the encouragement of young men and women to travel abroad and engage in acts of terrorism,” he said. “This is a phenomenon which has greatly increased. It's a matter of great and justified public concern. You were disseminating such material on a massive scale.”

Esayed admitted that she had written the tweets but her lawyer argued that she had not provided any practical assistance to terrorists.

“The material that you were disseminating encouraged young men to go to fight,” the judge responded. “Furthermore to encourage women to go to support them and indeed to bring up their children in the belief that it is their duty to take up arms, to wage violent jihad and embrace martyrdom. And furthermore to encourage mothers to be proud of their sons who die as martyrs.”

In Northern Virginia, meanwhile, an honors student was operating a similar Twitter account. Casual observers who heard Amin talking to his friend Reza Niknejad, 18, would have thought they sounded like any other sports obsessed teenagers.

The FBI, however, says they spoke to each other in code: “basketball” was jihad, a “basketball team” was a jihadist organization, and “Syracuse” stood for Syria.

Amin’s case is a little different from his colleague’s in London as he is also accused of helping his friend Niknejad travel to fight with ISIS. He drove his fellow Prince William County schoolboy to Dulles Airport in January and put him on a plane to Turkey where he was met by one of Amin’s contacts and taken to Syria.

FBI agents had been tracking Amin since the previous November. He operated the @AmreekiWitness Twitter account, which supported the so-called Islamic State and engaged in repeated online spats with the State Department’s official counter-radicalization Twitter account Think Again Turn Away (@ThinkAgain_DOS)

Rita Katz, the director of the SITE Intelligence Group, mocked the State Department for engaging in these disputes in TIME magazine last September. “Think Again Turn Away’s involvement in counterproductive conversations has been a regular occurrence for some time now,” she wrote.

One exchange highlighted the State Department replying to Amin’s tweet of August 6. “IS has flaws, but the moment you claim they cut off the heads of every non-Muslim they see, the discussion is over,” he said.

Think Again Turn Away replied: “#ISIS tortures, crucifies & shoots some- ISIS also gives ultimatums to Christians: convert, pay or die- Some flaws u say?”

Amin’s account, which had over 4,000 followers, tweeted more than 7,000 times. He pleaded guilty to charges of conspiring to provide material support and resources to ISIS.

Dana J. Boente, U.S. Attorney for the Eastern District of Virginia, said the arrest and conviction proved that law enforcement agencies would now crackdown on jihadi propagandists.

“[The] guilty plea demonstrates that those who use social media as a tool to provide support and resources to ISIL will be identified and prosecuted with no less vigilance than those who travel to take up arms with ISIL,” he said.

Amin is scheduled to be sentenced on August 28