DALLAS (CBSDFW.COM) – In a tweet Monday, Governor Greg Abbott revealed the shooter responsible for the deadly shooting in Odessa previously failed a background check to buy a gun in Texas.

In the same tweet, the Governor said the killer didn’t go through a background check for the gun he used in Saturday’s shooting.

The Governor did not reveal other details and a spokeswoman for the Texas Department of Public Safety didn’t return a call from CBS 11.

Mr. Abbott has said he and his office, along with state agencies can take action to make the state safer without the legislature.

Governor Greg Abbott (CBS 11)

One area Republicans and Democrats agree on is ensuring the background check system is accurate and continuously updated.

But there’s still disagreement whether to expand background checks to include stranger to stranger gun sales.

Former Republican State Representative Matt Rinaldi of Irving said Monday, “In the absence of any evidence that there’s an issue or has been in the past mass shootings, I don’t think there’s any reason to change who the background check system applies to. A vast majority of purchases including at gun shows are subject to federal background checks.”

State Representative Chris Turner of Grand Prairie and Chair of the House Democratic Caucus said Monday, “Republicans still opposing closing the loophole, stranger to stranger gun sale loophole, is a huge problem. I think that’s what the American people expect us to solve and the people of Texas expect us to solve. There’s no reason we can’t close that loophole.”

Governor Abbott has said another idea he and state leaders, various law enforcement officials, and mental health experts have discussed to prevent mass shootings focuses on a red flag law.

They would give authorities the ability to seize firearms from people once an official warning of danger comes in.

Rinaldi said, “I hope the Governor doesn’t support it. I hope that if he does, that he ensures that there are proper due process protections in place such as the person having the ability to defend themselves in court against any accusations.”

He said whether Republicans would support a red flag law will depend on the Governor.”

Turner said he supports such a law. “They need to be able to go to a judge right then immediately to be able to remove the firearm so that person doesn’t injure or kill someone else or themselves that’s what we’re trying to solve the due process has to be a part of that.”

The Governor is working on potential solutions to prevent mass shootings and domestic terrorist attacks but has resisted calls by some Democratic state lawmakers for an emergency special session.

Rinaldi said, “We want to ensure that Texas is as safe as possible but we don’t want to make any big change that may have unintended consequences of leaving people on able to defend themselves.”

Turner said, “I hope that if something positive is to come out of these two horrible tragedies that have affected our state these past few weeks that our Republican colleagues will see that they time to act is now I will actually be able to get something done.