NEW YORK — A man's masked face caught peering at a camera from the back of a taxi. Monopoly money in a backpack ditched in Central Park. And bullet casings with words scrawled on them.

Those are just a few of the details that the New York Police Department has released to the public in the five days since a masked gunman fatally shot the chief executive of a health insurance company in Manhattan.

The evidence has painted a picture of a "fully masked" suspect who appeared to have planned his movements with precision, but law enforcement is "on the right track," Mayor Eric Adams told ABC News' New York station WABC on Sunday.

"As I say, the net is closing and closing," Adams said. "This was an extremely challenging investigation. A fully masked person. The amount of detective work it took to put the pieces together -- we feel we're getting closer and closer."

As the manhunt continued for the suspect, whom investigators have not publicly identified, police in New York and elsewhere said they were still looking for evidence in Wednesday's fatal shooting of UnitedHealthcare CEO Brian Thompson in New York City. The NYPD believes it is making good progress toward identifying the suspect, but has so far not done so, sources told ABC News.

NYPD detectives arrived on Saturday in Georgia. Investigators have said the suspect took a bus to New York, arriving on Nov. 24 from Atlanta, although it was unclear if his travels began in that city. And the FBI is assisting the nationwide manhunt, according to law enforcement sources.

Back in New York on Sunday, members of the New York Police Department's dive team were again searching underwater in the Central Park. They were seen in the water near the Bethesda Fountain.

The masked gunman shot Thompson at point-blank range at 6:44 a.m. on Dec. 4 outside the New York Hilton Midtown, where Thompson's company was holding an investors conference. NYPD Commissioner Jessica Tisch described the attack as "brazen" and "targeted." The suspect is thought to have left the scene of the shooting and taken a bike north into the park.

Adams on Sunday declined to comment on specific evidence, saying only that "every piece is important." And he spoke generally about the ongoing underwater search.

"Everywhere is important. Everyplace is important," Adams said, adding a moment later, "It's dark down there, you know."

The backpack had been found nearby in Central Park. Police have not yet recovered the distinctive gun used in the shooting.

The suspect took a taxi to the Port Authority bus facility at 178th Street and boarded a bus out of New York City following the shooting, according to police.

NYPD officials released images on Saturday that they said were of the suspected shooter. The man appeared to have been in the back of a taxi, where he could be seen peering through the open slider in the partition between the seats. Another photo appeared to show the man walking by the window of a cab. It was unclear when the photos had been taken.

Investigators believe they secured DNA samples from several pieces of evidence discovered at or near the crime scene, law enforcement sources told ABC News. The DNA samples are currently at the NYC Office of the Chief Medical Examiner to be run through databases for a possible match -- a process that could take several days, the sources said.

Police were also able to extract a fingerprint off a water bottle the suspect bought at a Starbucks. The print is smudged, so it is unclear whether it will be helpful to the investigation, sources said.

"I don't want to do anything that's going to tip him off that we're on his trail, but we feel really good where we are," Adams said on Sunday. "Finding the knapsack, getting the cab photos, looking at some of the evidence that we have available to us, we feel really good where we are."

ABC News' Aaron Katersky, Mark Crudele, Bill Hutchinson, Jon Haworth, Ivan Pereira and David Brennan contributed to this report.

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