By Faith Karimi and Darran Simon, CNN

(CNN) -- For two decades, Joseph James Pappas has held a grudge against the Houston cardiologist who performed the surgery that left his mother dead on the operating table, police say.

Pappas, 62, planned Dr. Mark Hausknecht's killing over his mother's death, and last month followed the doctor as he rode his bicycle to work at Houston Methodist Hospital, according to authorities.

Both men were on their bikes on July 20 when Pappas rode past Hausknecht before turning around and fatally shooting him, police said.

The prominent surgeon and former cardiologist for President George H.W. Bush was found near a construction site with hundreds of workers, but the equipment was loud enough to mask the sounds of gunfire.

"It appears that this may be a 20-year-old grudge that this man held," Police Chief Art Acevedo said Wednesday. "There was a lot of planning that went into this. There was a lot of planning and sadly some skill."

Police issued an arrest warrant for Pappas after they searched his home and did not find him. The suspect has multiple firearms and has made phone calls indicating he was considering suicide, Acevedo said.

"This man is dangerous, this man is capable, this man has some skills (with firearms)," he said.

Hausknecht's family released a statement Thursday thanking Houston police and others who helped identify a suspect, and asking the public to focus on Pappas' photo and contact police if they know where he is.

Surveillance video helped identify him

In the days following the shooting, the motive and the suspect's identity remained a mystery. Police said the doctor was likely targeted and implored witnesses to come forward with any information.

Stunned friends and neighbors canvassed the area where police believe the gunman may have fled. They encouraged residents to look through their security camera footage for images of the suspect.

Surveillance video obtained by a neighbor allowed investigators to enhance the suspect's photo, which helped identify him, police said. On Tuesday, someone said they recognized the suspect in surveillance video released a day before.

Suspect's number is linked to firearms website

Acevedo said there's other evidence that leads them to believe Pappas is the shooter, but did not provide additional details. Other surveillance images showed the suspected gunman just behind Hausknecht as both headed north on a street, police said.

Police posted images on Twitter in which Hausknecht is highlighted with a green circle and the suspect with a red circle.

CNN called a phone number listed for Pappas' real estate company Wednesday, but the call went to voice mail.

That phone number is linked to recent listings on a firearms auction website for several guns, ammunition, tactical vests and ballistic plates for car doors. The posts, from a user in Houston, apparently went online days after the shooting.

It is unclear whether any of the firearms listed online were used in the shooting. A spokesman for Houston police declined to comment on the ads.

Suspect worked as a constable for decades

Pappas worked for 30 years as a constable, according to Texas Commission on Law Enforcement records. He worked for Harris County as a peace officer and a reserve officer from May 1983 to July 2013.

Pappas took law enforcement classes through August last year, and appeared to own multiple guns, police said.

Doctor remembered as quiet and friendly

Hausknecht and his wife, Georgia Hsieh, lived in an upscale neighborhood not far from the Texas Medical Center in southwest Houston. In addition to his wife, who is a retired emergency room physician, Hausknecht is survived by two adult sons, Matthew and Paul.

Friends and colleagues remembered him as a quiet, generous and kind person.

"The man who healed so many hearts during his life, has left so many broken by his death," a Houston Chronicle obituary read.