President Donald Trump on Sunday said that a mass shooting that took place a day earlier in Texas "really hasn't changed anything" about how lawmakers are approaching gun control legislation.

"We are in the process of dealing with Democrats and Republicans, and there’s a big package of things that’s going to be put before them by a lot of different people I’ve been speaking to a lot of senators, a lot of house members, Republicans, Democrats — this really hasn’t changed anything, we’re doing a package and we’ll see how it comes about," Trump said outside of Marine One. "That’s irrespective of what happened yesterday in Texas."

"Over the last five, six, or seven years, no matter how strong you need the background checks, it wouldn’t have stopped any of it," he claimed.

Authorities on Sunday were still piecing together information about Saturday's attack around Odessa, Texas, where a gunman opened fire at random following a traffic stop, killing at least seven people and injuring 22 people. Police have not publicly confirmed the suspect's identity, but they said he used an AR-type weapon.

The attack was the second major mass shooting in Texas in recent weeks after a gunman in early August opened fire on an El Paso shopping area, killing 22 people. The suspected shooter appeared to have posted an anti-immigrant screed online prior to the attack.

Trump administration officials, Republicans and Democrats were pressed on the latest shooting on the Sunday political talk shows. Acting Homeland Security Secretary Kevin McAleenan told ABC's "This Week" that such attacks should "absolutely" be considered "a homeland security threat."

"They absolutely are a homeland security threat," McAleenan said. "In our counterterrorism strategy and approach, domestic terrorism has taken a front line focus for us."

McAleenan pointed to the formation earlier this year of an office focused on "targeted violence and terrorism prevention, with an explicit focus and balance on domestic terrorism, including racially motivated violent extremism, which we’ve seen much too much of in the recent weeks and months."

Meanwhile, former Texas Rep. Beto O'Rourke, a Democratic presidential contender, called the amount of mass shootings in the U.S. "f---ed up."

"The rhetoric that we've used, the thoughts and prayers that you just referred to, it has done nothing to stop the epidemic of gun violence," O'Rourke said on CNN's "State of the Union." "To protect our kids, our families, our fellow Americans in public places. At a Walmart in El Paso, where 22 were killed. At Southerland Springs, in a church, one or two a day all over this country. A hundred killed daily in the United States of America. ... No other country comes close."

On CBS's "Face the Nation," O'Rourke called for universal background checks, red flag laws and buying back weapons like the AR-15 from owners.

"We've got to follow the lead of those moms who demand action, the students who are marching for our lives, who themselves have announced ambitious plans to ensure that we can protect one another and that our kids don't have to fear going to school or the future of this country," he said.

On NBC's "Meet the Press," former Housing and Urban Development Secretary Julian Castro, also a Democratic presidential candidate, said he would "maximize executive authority" to combat gun violence and push to put "as much pressure" as possible on swing state Republican senators in hopes of getting to a compromise gun control bill.

Also on "Meet the Press," Sen. Rick Scott, R-Fla., said the problem involving gun violence is "there's too many people that have mental illnesses that we're somehow not addressing and they have access to weapons and they shouldn't."