The suspect, Joseph James Pappas, 65, is now wanted on an arrest warrant and is considered to be suicidal and unsafe.
The individual may have been seeking revenge for his mother, who died during an operation performed by the doctor over 20 years ago, authorities have said.
"The suspect had not been heard from by people that know him for over 24 hours and there is a text that he sent someone that said he was going to kill himself", the police chief said.
"There was a lot of planning that went into this, and sadly, some skill", Acevedo told reporters.
The man suspected of killing a Houston cardiologist was a former law enforcement officer who recently tried to sell several guns and ammo.
Three days after the July 20 attack on Dr. Mark Hausknecht in Houston, Jeanette Spencer received notification in the mail indicating that the home of family friend Joseph James Pappas had been deeded to her.
Hausknecht was fatally shot on July 20 as he rode his bicycle to work at the city's bustling medical center, when a man also riding a bicycle fired at least two shots at him before pedaling away.
A neighbor called in the disturbance around 9 p.m. when they noticed that a back gate was open and they thought they saw Pappas, police said.
Police searched his home at 4 a.m., August 1, and have been in contact with Spencer.
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Among those patients was former President George H.W. Bush, who appeared next to Hausknecht during a 2000 news conference at the hospital after being treated for an irregular heartbeat.
"He's considered to be armed and unsafe". An arrest warrant for murder subsequently was issued, the chief said.
Other surveillance images showed the suspected gunman just behind Hausknecht as both headed north on Main across West Holcombe Boulevard, police said.
"We need to find this guy".
Cops had previously released surveillance images of the shooting, which occurred as Hausknecht was riding a bicycle to work, and shared eyewitness testimony of the shooting.
The doctor was shot three times - twice in the torso and once in the head.
"Mark was a fantastic cardiologist and a good man".
The former president offered his condolences to the family in a written statement. "I will always be grateful for his exceptional, compassionate care".
According to real estate website Har.com, a man with the name Joseph James Pappas is listed as "a licensed real estate service provider in Houston, Texas", and he owns the Pappas Realty Company.