WATCH: White House blames Texas for death of National Guardsman while rescuing drug-smugglers

Fox News reporter Jacqui Heinrich pressed Psaki to comment Monday on the drowning of 22-year-old Texas Army National Guard Specialist Bishop E. Evans.

Jacqui Heinrich asked at a press briefing if the White House bears responsibility for the young National Guardsman's death given that the surge of illegal migrants overwhelming the United States-Mexico border has been one of many crises plaguing the administration since President Joe Biden took office.

"I would note that the National Guard works for the states, so he is an employee of the Texas National Guard, and his efforts and his operation were directed by there, not by the federal government in this effort and this apparatus," Psaki answered.

Psaki maintained that "we have long-stated that our immigration system is broken," adding that there "needs to be more done to invest in smarter security, to have a more effective asylum-processing system." Psaki further offered, "And we would welcome any efforts for any elected official to work with us on that."

At another point during the presser, Psaki claimed that former President Donald Trump invested "billions of dollars in a border wall that was never going to work or be effective."

Many critics of the administration have linked the chaos at the border to Biden-era policies, such as halting border wall construction and rolling back the Migrant Protection Protocols (MPP) program known as "Remain in Mexico."

During the exchange, Psaki was grilled over what the federal government might do in the future to help manage Biden's border crisis. Heinrich cited local border communities as well as state leadership who've requested more assistance and manpower from the federal government to resolve the issue hitting close to home.

"If we just dial it back a few years to kind of what we inherited here, the former president invested billions of dollars in a border wall that was never going to work or be effective," Psaki said, "instead of working towards comprehensive immigration reform." She said that Biden proposed investing in "smarter" security at the border, "something he'd be happy to work with governors on and certainly we're open to having that conversation whenever they're ready to do that."

Bishop's body was recovered Monday after a multi-day interagency search. He went missing and was presumed dead following the rescue attempt Friday.

Gov. Greg Abbott (R-TX) released a statement on social media Monday:

"We are heartbroken to learn of the death of SPC Bishop Evans. He heroically served his state & country. I want to thank all rescue teams that worked to locate this soldier. Join me & Cecilia in praying for the family & friends of SPC Evans."

"Our National Guard soldiers risk their lives every day to serve and protect others, and we are eternally grateful for the way SPC Evans heroically served his state and country," Abbott expressed in the press release on Bishop's death.

The two illegal immigrants that Evans was attempting to rescue were "involved in illicit transnational narcotics trafficking," according to the Texas Military Department. The pair remain in the custody of US Customs and Border Patrol.