(CNN) -- The police chief of Tulsa, Oklahoma, offered a stern, succinct message Saturday to the man he believes killed three people and critically wounded two others in a spate of seemingly random shootings: "We're coming for you."
Chief Chuck Jordan described the shootings at four separate sites -- all of which occurred early Friday within two to three miles of each other -- as "vicious and cowardly attacks."
A survivor described the suspect as a white man, driving an "older" white pickup truck, according to Jordan. Police Capt. Jonathan Brooks told CNN that such a truck had been spotted at at least three of the shooting sites, around that time.
Still, Jordan indicated authorities do not know the identity of the shooter. He added, too, that a basic description of a white man driving a white truck "alone probably accounts for 50,000 people in the city of Tulsa."
With the assailant still at large, city leaders stressed that information from the public will be critical to cracking this case.
"To know that you can't walk down the street at night in your own neighborhood, that's a terrible thing," said city councilor Jack Henderson, who represents the district where the shootings occurred. "The only way that this person is going to be brought to justice is we need some leads. We need some people to come forward. We need some people to tell us what you know, what it is you heard."
About 30 representatives from four different law enforcement agencies -- the Tulsa police, Tulsa County Sheriff's Office, the U.S. Marshals Service and the FBI -- are on the case, as part of a newly formed task force called "Operation Random Shooter."
They'll be working around the clock to solicit leads, gather evidence and conduct interviews, according to Jordan.
Earlier Saturday, Tulsa Mayor Dewey Bartlett told CNN that at least 40 cruisers are patrolling the affected area. He added that officers are spending the weekend "going, literally, door to door, and asking people if they have seen anything (and) what their opinions and observations are."
What authorities do know is the first shooting occurred at 1:03 a.m. Friday, according to Brooks of the Tulsa police. That victim, 49-year-old Dannaer Fields, died at a hospital.
Three minutes later, two people were shot nearby -- one of them "pretty close to the (gunman's) vehicle and the other ... a little further away," the police captain said. Those two were initially in critical condition but, by Saturday evening, were believed to have improved to stable and are expected to survive, according to Brooks.
Then, just before 2 a.m., a fourth shooting incident -- like the first, a fatal -- occurred. The third person killed was found around 8 a.m. next to a funeral home in a more commercial district, though Brooks said police believe he was shot much earlier.
In addition to Fields, Jordan identified the other two victims as William Allen and Bobby Clark.
"It appears all the victims were out walking or in the yard," Brooks said. "This (happened in) a residential neighborhood, predominantly single-family dwellings, except for the last victim."
All the victims were black.
The Rev. Warren Blakney, a pastor at a city church and president of the NAACP's Tulsa branch, said the shootings could well prove to be hate crimes given that they happened in a predominantly African-American neighborhood.
"For a white male to come that deep into that area and to start indiscriminately shooting, that lends itself for many to believe that it probably was a hate crime," Blakney told CNN.
Brooks, the police captain, said one survivor recalled how "the suspect drives up to him, asks ... for directions and shoots him for no reason." There is no indication the shooter used a racial slur or said anything else that might indicate his motive, according to police.
Jordan acknowledged it is a "very logical theory" to assume they were targeted in hate crimes, but said that "we have had no evidence" yet to indicate that.
"Right now, I'm more worried about three of my citizens being murdered," the chief said. "And if it takes us in a direction of a hate crime, that's certainly where we'll go and we'll prosecute him for that as well."
Tulsa's mayor commended city residents for already having "really come together," intent on helping capture the killer.
"It should be concerning to all Tulsans, because we are all in this together," Bartlett said. "Some of our fellow Tulsans have been pretty violently shot, and some of them are not here today to enjoy the weekend with their families."