Texas school shooting: Suspect's grandmother upgraded to good condition

The Uvalde City Council meeting scheduled for Tuesday has been canceled so community members can continue to grieve, Uvalde Mayor Don McLaughlin announced.

"Our focus on Tuesday is on our families who lost loved ones," McLaughlin said in a statement Monday. "We begin burying our children tomorrow, the innocent victims of last week’s murder at Robb Elementary School."

McLaughlin reiterated that the investigation into the shooting is being conducted by the Texas Department of Public Safety, saying that statements made by Texas Lt. Gov. Dan Patrick on Saturday that he was "not told the truth" about the timeline of events during the shooting are not true.

"Local law enforcement has not made any public comments about the specifics of the investigation into the incident or mislead anyone," McLaughlin said.

McLaughlin also thanked the U.S. Department of Justice for accepting his request to conduct an independent review of law enforcement’s response to the mass shooting, adding that the families of the victims “deserve answers, and the truth will be told.”

-ABC News' Jenna Harrison

Bipartisan talks to reform gun safety laws are continuing even though members of Congress are out on recess.

Sen. John Cornyn, R-Texas, told reporters in San Antonio Monday, "We’re already having those discussions in person and on the phone. Look forward to meeting on Tuesday through a Zoom call to try to see if we can agree on a basic framework about how we go forward."

Cornyn’s Democrat counterpart, Connecticut Sen. Chris Murphy, tweeted that he spoke with senators from both parties Monday "trying to find the common denominator on a gun violence bill."

"Senator Schumer has given us just over a week to find a compromise. This time, failure cannot be an option," Murphy tweeted.

-ABC News' Trish Turner

The two injured adults who remain hospitalized at the Brooke Army Medical Center have been upgraded to good condition, the hospital said Monday.

Three other survivors remain at University Hospital: a 10-year-old girl in serious condition, a 9-year-old girl in good condition and the suspect's grandmother who is in fair condition, according to the hospital.

Seventeen people overall were injured in Tuesday's mass shooting.

-ABC News' Jennifer Watts

As President Joe Biden arrived at the White House Monday, he said he met with victims and their families Sunday for three hours and 40 minutes, adding that their "pain is palpable" and "unnecessary."

The back-to-back mass shootings in Buffalo, New York, and Uvalde, Texas, prompted a group of bipartisan senators to engage in some initial conversations about gun legislation. Biden said he hasn't spoken to Republicans about gun reform. Asked by a reporter if he thinks anything will now be different for Republicans, Biden said he did not know, but that he believes they’ll "take a hard look."

Noting that he has asked for Congress to act on guns, a reporter asked Biden if he has a particular responsibility now to get this done. Biden said he’d continue to take any executive action he can, but admitted that without Congress, he "can't outlaw a weapon" or change background checks.

-ABC News' Armando Tonatiuh Torres-García