The Secret Service had the former F.B.I. director, James B. Comey, followed by law enforcement authorities in unmarked cars and street clothes and tracked the location of his cellphone the day after he posted an image on social media in May that President Trump’s allies said amounted to a threat to assassinate the president, according to three government officials.

Mr. Comey and his wife, Patrice, were tailed by the authorities as they drove from the North Carolina coast, where they had been vacationing, through Virginia to their home in the Washington area, the officials said, describing the details of the surveillance on condition of anonymity because they did not want to be identified discussing a federal investigation.

At the same time, the Secret Service was receiving information showing the location of Mr. Comey’s phone while federal authorities were stationed at his home waiting for him to return, the officials said.

The intense surveillance occurred a day after Mr. Comey, long perceived by Mr. Trump as an enemy, had posted a photo on social media of seashells he had found while he walked on the beach. The shells were arranged in the formation “86 47,” combining a slang term meaning to dismiss or remove with the numerical designation of Mr. Trump’s second presidency. Trump critics have often displayed the phrase on signs and clothing at protests.

T-shirts saying both “86 47,” referring to Mr. Trump, and “86 46,” referring to former President Joseph R. Biden Jr., are available for sale on Amazon.

Shortly after the image was posted, Donald Trump Jr. wrote on social media that Mr. Comey was “casually calling for my dad to be murdered.” The accusation created a firestorm online, as Mr. Trump’s supporters accused Mr. Comey of plotting to assassinate the president.