President Joe Biden and first lady Jill Biden have arrived in Uvalde, Texas, Sunday morning and plan to meet with loved ones of 19 students and two teachers killed in Tuesday's mass shooting at Robb Elementary School.

The Bidens arrived at Uvalde's Garner Field on Marine One just before noon after flying on Air Force One at Kelly Field in San Antonio earlier Sunday.

The Bidens were met on the tarmac at Garner Field by Texas Gov. Greg Abbott, Uvalde Mayor Don McLaughlin and other local dignitaries.

The White House said the president and first lady intend "to grieve with the community that lost twenty-one lives in the horrific elementary school shooting."

The Bidens are scheduled to visit a growing memorial outside Robb Elementary School and attend Mass at a local Catholic church before meeting with the family members of those killed in the attack and first responders.

Some Democrat and Republican senators are negotiating through the Memorial Day weekend in an attempt to find "common ground" on potential federal gun laws intended to prevent massacres like the one at a Uvalde, Texas, school, according to Connecticut Sen. Chris Murphy.

"There are serious negotiations and we are going to continue to meet through early next week to try to find some common ground," Murphy, a Democrat, told ABC "This Week" co-anchor Jonathan Karl on Sunday.

Murphy said negotiations with Republican senators have included discussions of "red flag" laws, expansion of the federal background check system, safe storage, mental health resources and increased security funding for schools.

"What we're talking about is not insignificant," Murphy said.

He said the goal is to come up with a package "that really in the end could have a significant downward pressure on gun violence in this country and break the logjam."

"Maybe that's the most important thing we could do is just show that progress is possible and that the sky doesn't fall for Republicans if it supports some of these common sense measures," Murphy said.

Murphy, who took up the cause of combatting gun violence a decade ago following the deadly 2012 mass shooting at Sandy Hook Elementary School in Newtown, Connecticut, said he is hearing from more Republicans than ever agreeing on the need for new federal gun legislation, or to bolster laws on the books now.

Republican Rep Adam Kinzinger, R-Ill., told Karl that "raising the age of gun purchase to 21 is a no brainer."

"If you look at the Parkland shooting, you look at Buffalo, you look at this shooting, these are people under the age of 21," Kinzinger said. "We know that the human brain develops and matures a lot between the age of 18 and 21. We just raised -- without really so much as a blink -- the age of purchasing cigarettes federally to 21."

Investigators have yet to find a specific triggering event that led the gunman to attack on Tuesday, or why he selected Robb Elementary School as the target, according to law enforcement sources.

Texas Department of Public Safety director Col. Steven McCraw also said Friday that a motive has not yet been determined.

A particular focus for the FBI is assisting Texas detectives in analyzing Ramos’ online communications and anything they could find that was left on his devices, the sources said.

McCraw said investigators plan to track down people with whom Ramos communicated online.

The FBI has deployed some 200 hundred personnel to Uvalde, including computer and cell phone analysts and digital forensic experts, in addition to providing remote support.

-ABC News' Pierre Thomas, Josh Margolin and Aaron Katersky

Alleged school shooter Salvador Ramos was in the classroom for 77 minutes before officers entered and killed him. During that time, he discharged 315 rounds of ammunition, with hundreds of those rounds fired within the first four minutes of his arrival, authorities said.

After the initial barrage, the police commander on the scene mistakenly believed the shooter was barricaded and it was no longer an active shooter incident, Texas Department of Public Safety Director Steve McCraw told reporters in an update Friday. But as officers gathered outside the classroom, the gunman kept shooting on at least six occasions, the new details show.

At 11:35 a.m., as the first three officers entered the building and approached classrooms 111 and 112, the suspect fired into the hallway through a closed door, where two officers sustained "grazing wounds," McCraw said.

He fired an additional 16 rounds two minutes later -- at 11:37 a.m. -- and again at 11:38 a.m., 11:40 a.m. and 11:44 a.m., according to McCraw, who did not specify whether the additional discharges were directed at officers in the hallway or at those inside the classrooms.

At 12:21 p.m., with as many as 19 officers then gathered outside the classroom, the suspect again fired at the closed door, forcing officers to "move down the hallway," McCraw said.

Despite those additional spurts of gunfire – and a 911 call from inside one of the classrooms alerting a dispatcher that eight or nine people remained alive -- officers did not enter the classroom and kill Ramos until 12:50 p.m., according to McCraw.

The police response to the shooting is now being investigated, Texas Gov. Greg Abbott said Friday.

-ABC News' Lucien Bruggeman

The Justice Department will conduct a critical incident review to examine the law enforcement response to last week’s school shooting in Uvalde, Texas, a spokesperson announced on Sunday.

The review is being conducted at the request of Uvalde Mayor Don McLaughlin and the DOJ will publish a report on its findings at the conclusion.

"The goal of the review is to provide an independent account of law enforcement actions and responses that day, and to identify lessons learned and best practices to help first responders prepare for and respond to active shooter events. The review will be conducted with the Department’s Office of Community Oriented Policing," the DOJ said in a statement.

“As with prior Justice Department after-action reviews of mass shootings and other critical incidents, this assessment will be fair, transparent, and independent. The Justice Department will publish a report with its findings at the conclusion of its review.”