The notification was sent on January 4 under a 1973 U.S. law called the War Powers Act, which requires a presidential administration to notify Congress within 48 hours of committing armed forces to military action or imminent actions.
The White House did not immediately comment on the notification, the details of which are classified, and it is not clear if a redacted version will be released to the public.
While most Republicans have praised Trump for his actions, many Democratic lawmakers have criticized the president for failing to seek advance approval or notify Congress of the attack, expressing concerns that it could lead the United States into a war with Iran.
The U.S. administration was expected to explain the circumstances, the authority under which the strike was undertaken, and the planned duration of the military mission.
The leading Democrat in the House of Representatives, speaker Nancy Pelosi, later said the notification “raises more questions than it answers.”
“This document prompts serious and urgent questions about the timing, manner, and justification of the administration’s decision to engage in hostilities against Iran,” Pelosi said in a statement.
“The highly unusual decision to classify this document in its entirety compounds our many concerns, and suggests that the Congress and the American people are being left in the dark about our national security,” she added.
Trump has said he ordered the attack to “stop a war” and that Soleimani had been in the process of organizing “imminent and sinister” attacks on U.S. interests and allies.
The 62-year-old Soleimani was commander of Iran’s elite Quds Force, the foreign arm of Iran’s hard-line Islamic Revolutionary Guards Corps (IRGC), which has been designated a foreign terrorist organization by the United States.