Special counsel Robert Mueller’s notification to the White House that President Trump isn’t an investigative target means that the collusion charges against him in Christopher Steele’s dossier are untrue, supporters say.

Mr. Steele, a former British spy paid in part by the Democratic Party, said Mr. Trump personally supported the Russian hacking of Democratic Party computers during the 2016 election season.

The president’s supporters say that if Mr. Mueller found evidence that the anti-Trump dossier was accurate or if it required further investigation, then he would not have given the no-target assurances to Mr. Trump’s legal team in early March.

“The dossier is crap,” said a Trump associate familiar with ongoing discussions for the president to sit down for questioning by Mr. Mueller. “None of the stuff about the president is true.”

Mr. Trump has long dismissed the dossier’s charges as fiction.

Some journalists and Democrats have embraced Mr. Steele and his product’s unproven claim of an “extensive conspiracy” between the Kremlin and the Trump campaign.

Mr. Mueller has been investigating suspected Trump-Russia collusion since May, and the overall FBI investigation is 22 months old. The dossier has played a major role in influencing how the FBI has targeted Trump people.

Its use has brought howls of protests from Republicans, who say the bureau is relying on wild charges from a Democratic operative determined to destroy Mr. Trump. Mr. Steele’s bills were paid by the Democratic National Committee and the Hillary Clinton campaign via the investigative firm Fusion GPS.

The Washington Times has identified in the 35-page dossier 10 specific collusion charges against Mr. Trump, his associates, a Russian businessman and a group of Russian bankers. The Times found none of them to be confirmed publicly at this point.

The most often quoted item about Mr. Trump, which he denies, is that he spent time with prostitutes in a Moscow hotel in 2013 and was thus vulnerable to Kremlin blackmail.

But Mr. Steele lodged far more serious charges for which Mr. Mueller apparently has found no basis. Mr. Steele, once posted in Moscow as an MI6 intelligence officer, relied on paid middlemen as his sources, who gleaned information from Kremlin figures.

Because of the arrangement, Republicans charge that it was the Clinton campaign that colluded with Moscow to influence the election.

Mr. Steele’s charges against Mr. Trump:

⦁ The Kremlin fed Mr. Trump “valuable intelligence on U.S. opponents, including Democratic presidential candidate Hillary Clinton for several years.”

⦁ An “ethnic Russian” close to Mr. Trump said there was a “well-developed conspiracy of co-operation between them and the Russian leadership.”

⦁ The WikiLeaks election operation to release Democratic Party emails stolen by Russia “had been conducted with the full knowledge and support of Trump and senior members of his campaign.”

⦁ Mr. Trump maintained a “regular exchange with Kremlin” for at least eight years “including intelligence fed back to Russia on oligarch activities in U.S. … Trump and his associates duly had obtained and supplied the Kremlin with this information.”

Former FBI Director James B. Comey, fired by Mr. Trump in May, testified to Congress that he told the president he was not under investigation. At that point in time, the FBI had possessed dossier information for months and used it to obtain at least one surveillance warrant on Trump campaign volunteer Carter Page.

The majority Republicans on the House Permanent Select Committee on Intelligence concluded last month that their investigation found no collusion between the Trump campaign and Russia.

Rep. Adam B. Schiff of California, the committee’s top Democrat, protested the move, saying he wants more witnesses to testify. Mr. Schiff has been a big supporter of Mr. Steele and his dossier.

The Washington Post first reported on Mr. Mueller’s no-target notification.

The Trump associate told The Washington Times that Mr. Mueller gave his assurance in early March as the prosecutor tried to secure a Trump interview as a final step in writing a report.

The Trump legal team, headed by private lawyer Ty Cobb, has provided mounds of documents to Mr. Mueller detailing intimate discussions between Mr. Trump and members of his legal staff, who also have testified.

Mr. Mueller has been looking into charges of Russia collusion as well as obstruction of justice in the firing of his friend, Mr. Comey.

J.D. Gordon, a former Pentagon spokesman and Trump campaign national security adviser, told The Times that Mr. Mueller’s notification confirms what a lot of campaign workers have been saying.

“Even though the discredited Steele dossier was riddled with patent falsehoods, it drove the collusion narrative which fueled the witch hunt of the century,” said Mr. Gordon.

He has testified three times to Congress as well as to the special counsel. He hasn’t been accused of any wrongdoing.

“Once a group of people are under investigation, anything and everything is fair game,” said Mr. Gordon, ticking off names of people who have pleaded guilty to charges other than collusion.

“Designations of targets, subjects and witnesses don’t mean much from a legal standpoint since a person’s status could change in a New York minute. It’s really quite the racket,” he said.

The Trump associate told The Times that Mr. Trump is a “subject” in the investigation.

“It’s meaningless,” the source said. “He’s a witness.”

The source said Mr. Mueller’s notification isn’t a ruse to persuade Mr. Trump to submit to an interview because “there is no case.”