failing to issue a warning before Jan. 6, despite a slew of social media posts that armed groups intended to come to Washington to protest the results of the 2020 election.

The Homeland Security Department this year allocated $77 million for state and local governments to train police officers and improve intelligence-sharing across states.

Separately, the agency doubled the number of grants for organizations developing projects to research prevention strategies, including “off boarding” those vulnerable to radicalization. The allocation of $20 million, which has not been awarded yet, comes after the Trump administration gutted the grants before restoring $10 million in the last year of his term.

But increasing funding and acknowledging the problem are merely first steps. The work of identifying people associated with domestic extremism and helping them disengage from violence remains daunting.

Previous efforts by law enforcement to enlist the help of community members had prompted concern that the federal government was trying to spy on minority communities.

The Biden administration’s new approach to the issue is trickling down to those on the front lines of dealing with domestic extremists.

During the Obama administration, Mohamed Amin Ahmed, who runs an anti-extremism nonprofit in Minneapolis, had considered applying for federal grants to support his efforts to make cartoon videos seeking to debunk the Islamic State’s appeals to children.

But he decided not to apply after learning that the funding was tied to a requirement that he report suspicious activity to law enforcement.

Mr. Ahmed is now creating videos to target followers of QAnon, the pro-Trump conspiracy theory. He said he was planning to apply for the new round of government grants, which are no longer linked to law enforcement.

“We’re trying to help and not be part of the surveillance state,” Mr. Ahmed said.

After the Capitol riot, anti-extremism efforts are caught in a thicket of difficult political and First Amendment issues. Interventions that aim to change political beliefs or seem aligned with Democrats could be ineffective at attracting far-right extremists to participate, experts said.

A program in New York City, which recently won a federal grant of more than $740,000, will focus on stopping people from committing politically motivated violence without trying to change their beliefs.

Richard Aborn, the president of the nonprofit organization overseeing the program, said that it would accept participants through referrals from law enforcement, including for people who have already been charged with crimes.

Individuals who qualify after a psychological evaluation would then participate in one-on-one therapy for several months. The program’s success would be measured by changes in the individual’s emotional state.

Mr. Aborn said he expected the pool of participants to include white supremacists, jihadists and people threatening mass shootings.

To identify individuals who are not on law enforcement’s radar, Mr. Aborn is planning to develop targeted advertisements that would be seen by people who, for instance, were conducting anti-Semitic searches online. Clicking the ads would direct them to the one-on-one intervention program.

“This is all a new space,” Mr. Aborn said. “None of us know with any certitude about how much progress we’re going to make.”

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