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

The U.S. Marshals said they never placed anyone in handcuffs, but they say they “maintained order and peace in the midst of the grief-stricken community that was gathering around the school," in a statement posted on Twitter.

U.S. Marshals arrived on scene from Del Rio, Texas, at 12:10 p.m., and the first deputy U.S. Marshal went into the school to assist BORTAC, the elite tactical CBP team that ultimately shot the alleged shooter, the statement said.

They came from 70 miles away and got the first call around 11:30 a.m., according to the statement.

“These Deputy US Marshals also rendered emergency trauma first aid for multiple victims,” the statement said.

"Additional Deputy U.S. Marshals were asked to expand and secure the official law enforcement perimeter around the school,” the statement said. “Our hearts are heavy with sorrow and sadness at this horrific crime. We send our condolences to all the victims and families affected by this tragedy."

Angeli Rose Gomez, a mother waiting outside for her children, told the Wall Street Journal she was one of numerous parents urging police and law enforcement officers to go into the school sooner, first politely and then more urgently. She said U.S. Marshals put her in handcuffs, and told her she was being arrested for intervening in an active investigation.

Angel Garza, the stepfather of one of the children killed in the shooting, ran to try to reach and help his child, and was restrained and handcuffed by a local police officer, Desirae Garza, the girl's aunt, recounted to the New York Times.