Tucson, Arizona (CNN) -- A bag that is believed to belong to Arizona shooting suspect Jared Lee Loughner contains the same kind of ammunition as was used in Saturday's massacre, the Pima County Sheriff's Department said Thursday.
"We got ammunition in there and it matches the type used in the incident," department bureau chief Richard Kastigar told CNN's "John King USA."
Kastigar said that other items in the bag "tell us that there is a relationship between what's in the bag, what happened Saturday, what his movements were leading up to that time."
Kastigar would not elaborate on what else was in the bag but said "it gives us some indication to where (Loughner) was and what he was doing."
The bag, discovered on Thursday, has been transferred to FBI custody for further analysis, according to Pima County Sheriff's Department spokesman Jason Ogan.
Police say Loughner's father, Randy, recalled that his son was carrying a black bag the morning of the shooting that left six people dead and another 13 wounded.
The bag was the subject of an argument with his father just hours before the attack, according to Pima County Sheriff's Department Capt. Chris Nanos.
The bag was found when a teenager walking his dog spotted it in a "wash," or dry river bed, near where Loughner's family lives on Thursday morning, Nanos said.
The teen then turned it over to a neighbor, who called police, Nanos said, adding that "We certainly believe this is the bag."
But two law enforcement sources said Thursday that a Qwest Communications worker turned over the bag.
One of the sources said a teenager approached a Quest technician with the bag and that the Quest employee contacted police, remaining in the area as investigators searched the scene.
"Qwest is working with law enforcement during the ongoing investigation," the company said in a statement Thursday.
On Wednesday, Kastigar said Loughner was carrying the bag early Saturday when he had a brief discussion with his father in the Loughners' front yard.
"The father asked him questions similar to 'What are you doing? What is that?' and Jared mumbled something back to his dad, and his dad said he didn't understand what was said," Kastigar said. "It was unintelligible, and then Jared left."
The elder Loughner got in his vehicle and tried to follow his son, but could not find him, he said.
The bag will be tested for DNA, fingerprints, hair -- anything that might link it to Loughner. Investigators also likely will show it to Randy Loughner to see if he recognizes it, Nanos added.
Several boxes of 9mm ammunition and receipts were found in the bag, a law enforcement source said Thursday.
The source did not indicate where the receipts were from, but CNN has previously reported that a law enforcement source said Loughner purchased ammunition at a Walmart store.
"There are other things in the bag, but I'm not going to discuss the specifics," Kastigar said Thursday. "We need to substantiate through others who might have been involved with what is in the bag how (things) got there."
Investigators believe Loughner spent the night at a Motel 6 the evening before the shooting, Nanos said.
Authorities would not say how they discovered that information, but say they recovered a credit card from Loughner after the shooting.
The processing of the crime scene was complete Thursday morning, authorities said, and cleanup efforts were under way before the shopping center reopened to the public.
Rep. Gabrielle Giffords, whom police said was the target of the shooting, remains in critical condition, but her doctors have been pleased with her progress.
Loughner, 22, appeared in a Phoenix federal courtroom Monday to formally hear the charges against him -- including two counts of murder, two counts of attempted murder and one count of attempting to kill a member of Congress. He is now in federal custody.
On Wednesday, Kastigar said Loughner had previous contacts with law enforcement, but none so alarming that authorities were concerned about what he might do.
Speculation that law enforcement had enough information about Loughner to stop the shooting is "completely untrue," Kastigar told CNN's "John King USA." "I couldn't underscore that more."
"The events that led up to what happened Saturday as they relate to law enforcement contact really do not add up in their totality to anything that would cause a police officer to say. 'This guy is going to go out there and shoot 20 people.' There's nothing there," Kastigar said.
The law enforcement contacts included episodes of underage drinking and possessing drug paraphernalia, which Kastigar described as "very minor occurrences or interactions with law enforcement." Kastigar also said investigators had found no evidence Loughner followed up on suggestions from Pima College officials that he seek mental health help for behavioral problems.
Pima County on Thursday released records saying that Loughner visited the Rio Nuevo One Stop career center in September, but was asked to leave because he was filming with a video camera and refused to turn it off despite being asked repeatedly. "He pulled a crumpled copy of the Constitution out of his pocket and waved it at me, saying it was his right," a staffer's report on the incident said.
Loughner's former community college also released records showing that he frightened fellow students and acted oddly in incidents throughout 2010. Pima Community College ultimately suspended him.
His history at the college included an incident in February in which he reacted strangely to a poem read in one of his classes and made comments about abortion, wars and killing people. Two months later, a library staffer reported he was making loud noises at the computer. Also, a teacher reported he became "very hostile" after being told his grade in a Pilates class would be a B.
The incidents and disruptions continued into fall, the records said, and college officials became concerned about Loughner's mental health. After an incident in September, a police officer delivered a suspension letter to him and recounted the events that had taken place. When the officer was finished, according to the report, Loughner responded, "I realize now that this is all a scam."
On Wednesday, the 9th Circuit Court designated a district judge in California to hear Loughner's federal case. Judge Larry Burns is a 2003 Bush appointee serving in the U.S. District Court for Southern California, based in San Diego. The next scheduled federal hearing in the case is January 24 in Phoenix.
All federal judges in Arizona have recused themselves from hearing the case. The chief federal judge in Arizona -- Judge John Roll of Tucson -- was among those killed in the Saturday shooting.
Mark Hart, spokesman for the Arizona Game and Fish Department, said Loughner was stopped by an officer for running a red light at 7:30 a.m. on the day of the shooting. He was given a verbal warning and released.
Kastigar added that investigators are now certain that Loughner acted alone. A "person of interest" they had been seeking identified himself to police. He turned out to be a taxi driver who dropped off the suspect at the shopping center, Kastigar said.
CNN's Bill Mears and Paul Vercammen contributed to this report.