Story highlights AP is reporting that a TSA officer killed during a shooting at LAX lay bleeding for 33 minutes

Authorities investigating the shooting did not respond directly to the report

Officials release joint statement saying various statements have been made, some untrue

Authorities investigating a shooting at Los Angeles International Airport asked for patience Saturday as they piece together details of the rampage that left a Transportation Security Administration officer dead.

The statement released jointly by federal and local authorities came one day after The Associated Press, citing two unnamed law enforcement officials, reported the slain TSA officer lay bleeding for 33 minutes because police had not declared the terminal safe for paramedics to enter.

Authorities have charged Paul Ciancia, 29, in the death of TSA officer Gerardo Hernandez, who was shot in the chest and abdomen during the November 1 shooting at Terminal 3.

The joint statement did not directly address the AP report, but it defended the actions of authorities that day.

"Command officers and airport administrators were faced with a wide range of important objectives, including conducting a complete search to rule out additional gunmen or explosives, identifying and treating all injured victims, and coordinating the needs of the thousands of arriving and departing travelers that were impacted by the incident," the statement said.

Federal and local authorities will offer no further comment beyond the statement while the investigation is ongoing, said LAPD spokeswoman Sally Madera.

The AP reported that while it was unknown when Hernandez died, officials were examining whether paramedics, who were reportedly held 150 yards away from the terminal by police, could have gone in earlier.

"Various statements have been made regarding the incident, some of which are untrue and others that merit serious consideration by our respective agencies," the Saturday statement said.

"Numerous actions are underway relative to this incident and the ensuing response."

According to the joint statement, authorities are conducting a federal criminal investigation and an officer-involved shooting investigation. An after-action work group is also analyzing all aspects of the "multidiscipline response."

Key findings of the investigations will be released when they are completed, it said.

Hernandez, 39, was the first TSA officer killed in the line of duty in the agency's 12-year-history.

According to authorities, Ciancia walked up to the TSA checkpoint where Hernandez was working and opened fire, shooting him "at point-blank range," according to a court document.

Ciancia then went up an escalator toward the security checkpoint, but returned to shoot Hernandez again after apparently seeing the officer move, the document said.

The rampage came to an end when authorities shot and wounded Ciancia, who has been charged with the murder of a federal officer and commission of violence at an international airport.