The gunman's grandmother, who was shot by the suspect just before the school shooting, has been upgraded to good condition, University Health said Tuesday.

Even though Congress is on recess, a small group of bipartisan senators will meet by Zoom Tuesday afternoon to speak about gun control, multiple sources told ABC News.

The meeting is expected to include Sen. Chris Murphy, D-Conn.; Sen. John Cornyn, R-Texas; Sen. Tom Tillis, R-N.C.; and Sen. Kyrsten Sinema, D-Ariz.

The meeting is not expected to include every senator who is part of the bipartisan talks. Discussion with the larger group is expected later this week.

-ABC News' Rachel Scott and Allie Pecorin

President Joe Biden said to reporters Tuesday: "I will meet with the Congress on guns." Biden didn’t provide more details or say when the meeting would happen.

Biden addressed his visit to Uvalde, saying, "I was down in Texas and people sat in a room, about 250 of them in a large room with me for almost four hours, nobody left ... until I spoke to every single person in that room. Every single person. They waited to the very end."

-ABC News' Ben Gittleson

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