White supremacists, like their Islamist counterparts, explicitly seek to use violence to create a climate of fear and chaos that can then be exploited to reshape society in their own image. Their recruitment videos share an emphasis on the lifestyle they purport to offer recruits — one of “purity,” militancy and physical fitness. While jihadis share beheading videos, right-wing extremists glory in the live streaming of the deadly attack on two mosques in Christchurch, New Zealand. While Islamic State supporters communicate through an online platform called Telegram, white supremacists tend to do so through another platform, 8chan…

Perhaps most disturbing of all, both groups have real-world war zones in which to learn combat. Jihadis had Afghanistan in the 1980s, the Balkans in the 1990s and Syria today. White supremacists have the war in eastern Ukraine, in which they are fighting on both sides. Dr. Kacper Rekawek, a scholar who has studied the matter, estimates that 17,000 people from 50 countries, including the United States and many of its allies, have traveled to fight in Ukraine. Those with ties to far-right militias in Ukraine include at least one of four Americans indicted on a charge of promoting the deadly violence at the Unite the Right rally in Charlottesville, Va., in 2017. The New Zealand mosque attacker claimed in his manifesto that he had traveled to Ukraine. What we know for sure is that during his attack he wore a flak jacket bearing a symbol of one of the country’s main ultranationalist groups…

The F.B.I. should follow MI5’s lead, with appropriate safeguards for our constitutional freedoms. But this can happen only if Congress updates our post-9/11 legislation to allow domestic terror groups to be designated in the same way as foreign ones. This will allow our law-enforcement agencies access to the full suite of monitoring tools and our prosecutors the ability to bring meaningful charges for aiding domestic terrorism.