(CNN) Four physicians -- experts in pediatrics, infectious diseases and health policy -- have a message for White House Press Secretary Sarah Sanders: Contrary to what she says, it's not clear that the federal government is doing everything it can to care for children crossing the border.

And they'd like to help her understand what the government could do better so more children don't die.

When asked Friday about the recent deaths of two migrant children in US custody, Sanders told reporters that it was "an absolutely tragic situation" and that "we are doing everything in our capacity to make sure that when people do come, that they're taken care of so we don't have these types of instances."

But the physicians say there are steps the government needs to take before Sanders can truthfully say officials are doing "everything in our capacity" to make sure children don't die.

"In her mind, she may think they're doing everything possible, but we can tell you, you're not doing everything," said Dr. Colleen Kraft, president of the American Academy of Pediatrics. "Look at the facts. The record shows us that more needs to be done."

Dr. Buddy Creech, a pediatric infectious disease specialist, said authorities need to do thorough reviews of the children's deaths before declaring that everything possible is being done to prevent more deaths.

"In hospitals, when someone has a tragic event, a near miss, a drug error, we don't lead with 'we're doing everything we can.' It's ideal to lead with 'let's make ourselves open to self-criticism to make sure that we're taking care of the people who come to us for help,' " said Creech, associate professor of pediatrics at Vanderbilt University Medical Center.

"The real tragedy would be to say we're doing everything we can when we're not," he added.

Internal reviews of the children's deaths are being conducted within the US Department of Homeland Security.

Here are three things the physicians say the government could be doing better.

Triage children more effectively

Over the past several years, the United States has seen a large influx of children coming across the border.

Before about 2013, about 90% of migrants apprehended at the border were adult men. In contrast, last month, 59% of apprehended migrants were families or unaccompanied minors, according to the Department of Homeland Security.

That means about 1,400 to 1,500 unaccompanied minors or family members are apprehended every day, according to the agency.

"This has created enormous strain on our resources as we tackle the issue of how to deal with large numbers of kids," said Andrew Meehan, US Customs and Border Protection's assistant commissioner for public affairs.

There's also been an uptick in the number of apprehended migrants who are ill, Homeland Security officials said at a briefing last week. They said border officers transport dozens of apprehended migrants to hospitals every day.

Taking care of children -- especially such a large number of children -- requires special training and expertise, said Kraft, president of the pediatricians' group.

"Children are not just little adults; they have a whole physiology all their own," Kraft said.

For example, she points out that children, much more than adults, can look fine but actually be quite ill.

"A child can be running around and playing while their little systems are breaking down," she said. "When they triage these children and they don't have that pediatric oversight and expertise, they're going to miss kids who don't look like they're ill when they really are."

Kraft said she was pleased that on Wednesday, Customs and Border Protection Commissioner Kevin McAleenan reached out to her to ask whether the American Academy of Pediatrics could become involved in giving guidance in caring for children. Details of that involvement have not been worked out.

In January and again in March, Kraft wrote to Homeland Security Secretary Kirstjen Nielsen to offer assistance from the pediatricians' group. She said she did not receive a response to either letter.

After the children's deaths, Homeland Security put in place several changes.

Children will receive a "more thorough hands-on assessment" as soon as possible after they're apprehended, and 16 Public Health Service Commissioned Corps officers have been deployed to perform medical screenings.

The US Centers for Disease Control and Prevention will look into the causes of migrants' illnesses and assess the risk of influenza at the border. The CDC is also sending two small field teams to offer suggestions for respiratory disease surveillance in Customs and Border Protection shelters in certain areas. Based on that surveillance, the CDC will evaluate the feasibility of using antivirals and flu vaccines.

Reconsider sending feverish children back into detention

On Christmas Eve, 8-year-old Guatemalan migrant Felipe Gómez Alonzo died in Customs and Border Protection custody.

That afternoon, a local hospital found that he had a 103-degree fever, according to an agency account of his care. Less than two hours later, the hospital released him, and he was returned to the detention facility.

Noting that schools and day care centers typically won't allow children back until they've been fever-free for 24 hours, the doctors CNN spoke with wondered why Felipe would so quickly be sent back to a facility where he could potentially infect other detainees and staff.

When asked at the press briefing about the feverish child's return to the facility, a Homeland Security official declined to comment, saying "there's an internal ongoing investigation regarding the decisions and other factors that went into this situation."

Creech, the infectious disease specialist, added that it will take some careful thought to figure out where to place a migrant child who's being discharged from the hospital with a fever, especially if Customs and Border Protection facilities aren't equipped to properly isolate a sick child.

"I accept the fact that there isn't an obvious answer to this problem, but that doesn't reduce how important it is," he said.

Advocate for children in government custody

On December 24, a border protection agent noticed that Felipe had "possible influenza symptoms," according to the agency's account of his illness. He was brought to a hospital in New Mexico, where he was diagnosed with a common cold and discharged.

He died seven hours later.

An autopsy showed that that agent's hunch was right: Felipe tested positive for the flu, which typically kills dozens of US children every year.

It appears from the agency's account of the child's care that he was not tested for flu while at the hospital.

When asked in the press briefing whether Customs and Border Protection agents questioned certain aspects of Felipe's care at the hospital, a Homeland Security official responded that "it was not the intent or the place of the Border Patrol agents with the child and the father at the hospital to second-guess the care of the medical providers."

Though the doctors interviewed for this story did not say the agents should have second-guessed the doctors, they noted that Customs and Border Protection, which employs medical professionals, could have asked questions about his care, just as parents are encouraged to do when their children are sick.

Dr. William Schaffner, a professor of preventive medicine at Vanderbilt, said it would have been reasonable to ask about a flu test, given that it was flu season and an agent had observed that the boy had possible symptoms of the flu.

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"There are two reasons for asking 'Are you sure he doesn't have the flu?' One is for the boy's own health. The other is because you want to know, 'Am I bringing a kid with flu back to this facility, where he could spread it to others?' " he said.

"He was in custody of Customs and Border patrol. They were in place of mom -- in loco parentis," Schaffner added, using the legal term for someone serving in place of a parent. "I don't expect border patrol agents to be medical professionals, but this whole process leaves a lot of questions."

Dr. Irwin Redlener, a pediatrician and professor of health policy and management at the Mailman School of Public Health at Columbia University, agreed.

"If I was running the training for agents, I'd say, you're acting as a parental surrogate and as such have to pay attention as if this were your own child," said Redlener, who wrote an opinion piece for CNN about the children's deaths.

"The government has taken custody of these children, and they have to own that responsibility. You can't just take custody without responsibility," he added.