The man was being held in the area of Altoona, Pennsylvania, about 375 kilometres west of New York City, the official said on Monday (Tuesday AEDT).
The official was not authorised to discuss details of the ongoing investigation and spoke to the AP on condition of anonymity.
(UnitedHealth Group)
The man was arrested after police received a tip-off that he was at a McDonald’s outlet near Altoona.
Along with the gun and the writings, police also found a silencer and a number of fake IDs, the law enforcement official said.
The man has not been charged.
Thompson, 50, was killed last Wednesday in what police said was a “brazen, targeted” attack as he walked alone to the Hilton from a nearby hotel, where UnitedHealthcare’s parent company, UnitedHealth Group, was holding its annual investor conference, police said.
The shooter appeared to be “lying in wait for several minutes” before approaching the executive from behind and opening fire, NYPD Commissioner Jessica Tisch said. He used a 9mm pistol that police said resembled the guns farmers use to put down animals without causing a loud noise.
Ammunition found near Thompson’s body bore the words “delay” “deny” and “depose”, mimicking a phrase used by insurance industry critics.
Monday’s development came as dogs and divers returned to New York’s Central Park while the dragnet for Thompson’s killer stretched into a sixth day.
Investigators have been combing the park since the Wednesday shooting and have been searching at least one of its ponds for three days, looking for evidence that may have been thrown into it.
But they had not yet found the gun or the shooter, nor had they identified him by name.
On Monday, K-9 units sniffed leaf-covered planters between walking paths in Central Park near where police found the shooter’s backpack. Farther along the path that police suspect he took through the park after the shooting, scuba divers geared up and started searching a pond for the third straight day.
Retracing the gunman’s steps using surveillance video, investigators say the shooter fled into Central Park on a bicycle at 60th Street and Center Drive, emerged from park without his backpack at 77th Street and Central Park West and then ditched the bicycle about 7am (9pm AEDT) near 85th Street.
He then walked a couple blocks and got into a taxi, arriving at 7.30am (9.30pm AEDT) at the George Washington Bridge Bus Station, which is near the northern tip of Manhattan and offers commuter service to New Jersey and Greyhound routes to Philadelphia, Boston and Washington, NYPD Chief of Detectives Joseph Kenny said.
The FBI announced late on Friday that it was offering a $50,000 reward for information leading to an arrest and conviction, adding to a reward of up to $10,000 that the NYPD has offered. Police say they believe the suspect acted alone.
Late Saturday, police released two additional photos of the suspect that appeared to be from a camera mounted inside a taxi. The first shows him outside the vehicle and the second shows him looking through the partition between the back seat and the front of the cab. In both, his face is partially obscured by a blue mask.
Through the park search, the NYPD has taken steps to minimise disruption to visitors, leading to an odd juxtaposition of joggers, tourists and an active crime scene.
On Monday, 50-metre section of the park was cordoned off with blue and white police tape, giving the divers an area to change and get in the water.
At one point, a group of about 30 French-speaking tourists followed a guide down a path, but they couldn’t go any further because of the police tape. Before turning back, many of them whipped out their phones to snap a photo of the divers.
