Texas leaders are under growing pressure to increase gun control measures in the face of data indicating the state leads the US in mass shooting deaths, while Republicans have steadily eased restrictions on weapons and cut mental health spending.

As the funerals of the 19 children and two teachers begin on Tuesday in the tiny, devastated southern Texas city of Uvalde, a week after a shooting at the elementary school, state Democrats – and some Republicans – are demanding a special legislative action.

Right-leaning Republican governor Greg Abbott has been asked to convene a special legislative session to weigh legislation, with state senate Democrats calling for increasing the age for buying any gun to 21.

They also want to mandate background checks for all gun sales, and regulate civilian ownership of high capacity magazines, the Austin ABC affiliate KVUE reported.

They are also calling for “red flag” legislation that would permit the temporary removal of guns from persons who present an “imminent danger to themselves and others” and are urging a law to require a “cooling off” period when buying a gun.

“We have to do something, man,” Democratic state senator Roland Gutierrez, whose district covers Uvalde, said to Abbott at a press conference. “Your own colleagues are telling me, calling me, and telling me an 18-year-old shouldn’t have a gun.”

The gunman who took a military-style assault rifle and a backpack of ammunition into Robb elementary school last Tuesday and shot his victims in two adjoining classrooms was a local 18-year-old, Salvador Ramos.

He reportedly had posted violent threats and boasted about guns on social media, and was shot dead by federal agents after local police waited for more than an hour in the hallway in what state authorities said was “the wrong decision”.

“We’ve asked for gun control changes. I’m asking you now to bring us back [for a special legislative session] in three weeks … this is enough, call us back, man,” Gutierrez said.

Several Texas Republicans are now also putting pressure on Abbott to act after the shootings in Uvalde. “Governor Abbott should call us into special sessions until we do SOMETHING The FBI or DPS [Texas department of public safety] BELIEVE will lessen the chance of the next Uvalde Tragedy,” Republican state senator Kel Seliger said in a tweet.

“We should hope and pray every day, but DO something,” Seliger added, without presenting any specific proposals, the Dallas Morning News noted.

Republican representative Jeff Leach tweeted his call for a special session, saying: “Texas lawmakers have work to do. Conversations to engage in. Deliberations & debates to have. Important decisions to make.”

Abbott has sole authority to summon lawmakers before the next legislative session starts in January 2023. He has said all options are on the table.

But Texas has responded to the many mass shootings to afflict the state in the last 15 years by loosening not tightening restrictions on the use of guns.

And data from Everytown for Gun Safety, the gun regulation advocacy, indicate that 201 people have been killed in mass shootings in Texas since 2009, significantly more than any other state.

California has suffered 162 such deaths, while Florida, the third most populous state, with 22 million people compared with 29.7m in Texas and 39.6m in California, has counted 135 such deaths, according to Everytown, which defines a mass shooting as one in which four or more people are killed, excluding the shooter.

It was not immediately clear whether Uvalde was included in the Texas toll. Texas also leads the US in school shootings, according to US News & World Report.

The Texas Tribune reported that state lawmakers relaxed gun laws during the last two legislative sessions, including the approval of permit-less carrying of firearms in 2021. Such easing of gun laws was approved less than two years after the Odessa and the El Paso mass shootings left 30 people dead.

Some rightwing Texas Republicans last week called for more guns.

“We know from past experience that the most effective tool for keeping kids safe is armed law enforcement on the campus,” US Senator Ted Cruz told MSNBC.

Ken Paxton, the Texas attorney general who faces felony fraud charges, voiced similar sentiments and predicted more mass shootings.

“People that are shooting people, that are killing kids, they’re not following murder laws. They’re not going to follow gun laws,” Paxton said on the far-right network Newsmax. “I’d much rather have law-abiding citizens armed, trained so they can respond when something like this happens because it’s not going to be the last time.”

Democrat Beto O’Rourke, who is running for governor and heckled Abbott at a press conference last week, tweeted about some of Texas’ recent mass shootings, saying: “Abbott should have acted after Sutherland Springs, after Santa Fe, after Midland-Odessa, after El Paso. He refused. Let’s vote him out and get to work saving lives.”

He also slammed the weakening of gun restrictions and made a mark during his failed bid for the Democratic 2020 presidential nomination by advocating a ban on assault weapons for the general public.

Abbott, meanwhile, placed the blame for the Uvalde carnage squarely on mental health concerns, at his first press conference after the attack.

But mental health advocates told ABC News that Abbott has neglected mental healthcare, saying that he moved money out of Texas agencies charged with providing services. CNN also reported on such budget cuts.

“We as a state, we as a society need to do a better job with mental health. Anybody who shoots somebody else has a mental health challenge. Period. We as a government need to find a way to target that mental health challenge and to do something about it,” Abbott said last Wednesday, the day after the shooting in Uvalde.

Debbie Plotnick, executive vice president for state and federal advocacy at the nonprofit Mental Health America (MHA), told ABC that mental health was a regular scapegoat. “Hate is not a mental illness … having a mental health condition does not make someone violent,” she said.

This spring, Abbott switched $210m away from the state agency that oversees public mental healthcare, towards funding a controversial security program at the US-Mexico border.