A U.S. Border Patrol agent stands in front of the border fence that divides the U.S. and Mexico in San Diego, California, the United States, Nov. 17, 2018. (Xinhua/Zhao Hanrong)

Biden pledged during the press conference that he is committed to transparency and providing media access to facilities run by the CBP and other agencies. He didn't give a timetable as to when that would happen.

There were nearly 5,000 unaccompanied migrant children detained in CBP facilities as of Tuesday, according to the latest data available. Hundreds of the kids have been in custody longer than what is legally allowed, with the average time hovering around 130 hours.

The CBP is supposed to transfer unaccompanied minors to the Department of Health and Human Services' (HHS) Office of Refugee Resettlement within 72 hours, but the HHS has been scrambling to find enough shelters, citing constraints related to the COVID-19 pandemic.

Biden argued that progress is being made in finding additional housing facilities for the child migrants who are allowed to stay in the country as their immigration requests are processed. He said Defense Secretary Lloyd Austin just informed him that some 5,000 beds at Fort Bliss Army post in El Paso, Texas, had been made available for sheltering the migrants.

"I can't guarantee we are going to solve everything," Biden said of the challenges his administration is facing on the border. "But I can guarantee we can make everything better. We can make it better. We can change the lives of so many people."