Visiting Houston on Friday, Biden told reporters that the message he was sending to Iran with the attack in Syria was "you can't act with impunity, be careful."
John Kirby, a Pentagon spokesman, said the airstrike targeting the two militias was intended to limit the group's capability of launching future attacks and send a "clear message" that the United States will protect its citizens.
Republican members of Congress have praised the airstrike as a check on Iran's support for attacks against American personnel in Iraq through proxy groups.
But the response from key Democratic lawmakers has been quite the opposite.
"Offensive military action without congressional approval is not constitutional absent extraordinary circumstances," Kaine said in a statement. "Congress must be fully briefed on this matter expeditiously."
Kaine has been a vocal critic of the use of America's military force in Iraq without congressional authorization, going as far as introducing legislation to replace the broad 2002 Authorization for the Use of Military Force with narrower restrictions.
"Congress should hold this administration to the same standard it did prior administrations, and require clear legal justifications for military action, especially inside theaters like Syria, where Congress has not explicitly authorized any American military action," said Democratic Sen. Chris Murphy of Connecticut.
Biden administration officials soon found themselves defending the strike's legality.
"As a matter of domestic law, the president took this action, pursuant to his Article II authority to defend U.S. personnel," Jen Psaki, the White House press secretary, told reporters.
"The targets were chosen to correspond to the recent attacks on facilities, and to deter the risk of additional attacks over the coming weeks," she added. "As a matter of international law, the United States acted pursuant to its right of self defense, as reflected in Article 51 of the U.N. Charter."
"I can assure you, and I spoke to the National Security team, that there was a thorough legal process and review in advance," Psaki said.
Kirby said Biden "was well within his legal right to order these actions," citing the same two legal authorities to Pentagon reporters. He noted that the Pentagon had notified Congressional leaders prior to the attack and had briefed additional members and staff on Friday.
Thursday's airstrike was carried out by two F-15E fighter aircraft that dropped seven precision-guided munitions that leveled 11 buildings in Abu Kamal, right on the border with Iraq. While the damage assessment continues, Kirby acknowledged "we have preliminary details about casualties on site."