At least three people wounded in a mass shooting at an Allen, Texas, outlet mall remained in critical condition on Sunday, according to police.

Four victims were taken to Medical City McKinney, a trauma center in McKinney, Texas, about seven miles from Allen. Three of the patients were in critical condition and one was listed in fair condition, according to a statement Sunday from the Allen Police Department.

Eight victims were killed in the attack and a total of nine people were injured, police said. The shooter, whose name has not been released by police, was confronted and fatally shot by a police officer.

Among the injured, one patient was transferred from Medical City McKinney to Medical City Plano and was in fair condition. Another patient was transferred to Medical City Children's Hospital in fair condition, police said.

"We are a strong and caring community and we want all of the victims and their families impacted by this tragedy to know that we will wrap our arms around you, and we are here for you," Allen Mayor Kenneth M. Fulk said in a statement released Sunday. "The City of Allen pledges to offer our complete support. We know you are grieving, we are grieving. Rest assured, the nation and the world are also grieving."

President Joe Biden is renewing his call for Congress to pass an assault weapons ban following Saturday's mass shooting at a Texas outlet mall.

"Yesterday, an assailant in tactical gear armed with an AR-15 style assault weapon gunned down innocent people in a shopping mall, and not for the first time. Such an attack is too shocking to be so familiar," Biden said in a statement released Sunday.

"And yet, American communities have suffered roughly 200 mass shootings already this year, according to leading counts. More than 14,000 of our fellow citizens have lost their lives, credible estimates show. The leading cause of death for American kids is gun violence," Biden said.

Biden argued that "some progress" has been made as a result of the Bipartisan Safer Communities Act, and his various executive actions, but blasted GOP lawmakers, saying, they "cannot continue to meet this epidemic with a shrug. Tweeted thoughts and prayers are not enough."

"Once again, I ask Congress to send me a bill banning assault weapons and high-capacity magazines. Enacting universal background checks. Requiring safe storage. Ending immunity for gun manufacturers. I will sign it immediately. We need nothing less to keep our streets safe."

Texas Gov. Greg Abbott said he plans to visit Allen, Texas, on Sunday afternoon as he argued in a TV interview that the mass shooting at an outlet mall there underscores the need to focus on addressing mental health issues.

“Texans are hurting today. And the people who are hurting the most obviously are the families of the victims, the families of lost loved ones, families who have a loved one who is injured and our main priority right now is to help and support those families in the Allen community," Abbott said on Fox News Sunday.

He said he is going to Allen on Sunday "to begin the process of providing hope and healing."

“But I can tell you there are questions that are lingering that the families want answers to. And that is why this happened? Why did that gunman do this? How did this happen? And I know that those families need answers as quickly as possible,” said Abbott, who praised the quick response of police in confronting the shooter and killing him.

Abbott was asked about new polling that shows strong support for background checks for gun purchases, increasing the legal age to buy a gun to 21 and requiring mental health checks for purchases. The governor said his state is also looking at legislation to address "easy solutions" to get guns out of the hands of criminals.

But overall, Abbott argued, the focus should be on the “long term solution” of addressing mental health.

As authorities work to determine a motive for the outlet mall shooting in Allen, Texas, one avenue investigators are exploring is whether this was an act of domestic terrorism, multiple law enforcement sources told ABC News.

The shooter wore patches or stickers on his clothing that raised suspicion he may have gravitated toward right-wing extremism, the sources said, though they added no motive has yet been established.

Federal agents were seen at a home in the Dallas area believed to be associated with the shooter, ABC Dallas affiliate station WFAA reported.

Federal investigators are already going through the suspect’s electronic devices and social media as they work to understand what led to the killing rampage, the sources said.

In addition to a rifle used in the shooting, sources said investigators recovered additional firearms in a vehicle associated with the shooter.

The Texas Rangers are the lead agency on the case with assistance from the FBI, ATF and Allen police.

ABC affiliate WFAA has obtained a search warrant return listing what was found by investigators at the suspect's home.

Among the items were three boxes of ammo and loose rounds, a knife in a holster, two holsters and silver-colored handcuffs, according to the search warrant listing obtained by ABC affiliate WFAA.

-ABC News' Josh Margolin