Mexican authorities have detained five people in connection with last week's fatal shooting of a U.S. Border Patrol agent, but U.S. investigators have not said whether they are suspects in the case.

The detainees were arrested within two days after Robert Rosas, a three-year agency employee, was shot multiple times by suspected smugglers near the border fence.

One of the men, Ernesto Parra Valenzuela, 36, who was identified as the shooter, was injured and carrying a 9-millimeter handgun, according to police in Tecate, Mexico.

Parra and the four other detainees -- believed to be immigrant smugglers and bandits who were near the crime scene Thursday night -- are being held at the federal attorney general's office in Tijuana.

In high-profile cross-border cases, the Mexican government frequently provides U.S. investigators access to suspects, but it is unclear whether U.S. agents have questioned the men.

The FBI, which is leading the probe, has a "strong interest" in the detainees, but is continuing the investigation on several other fronts.

"We don't want the public to think this case has been solved. We consider the investigation ongoing," said Darrell Foxworth, an FBI spokesman in San Diego.

He said investigators are communicating with Mexican authorities and are closely monitoring the situation.

More than two dozen investigators from five federal and state agencies are working on the case, Foxworth said.

Cross-border probes are fraught with potential legal and political complications.

After the arrest last year of a suspect in the death of another U.S. border agent, Mexican authorities released him, saying their U.S. counterparts hadn't filed an extradition request. The man was later rearrested in Mexico.

Mexican authorities appear to be cooperating in the Rosas case.

They permitted Border Patrol K-9 units to cross the border to try to track down suspects and allowed U.S. helicopters to sweep the Mexican countryside with high-powered searchlights, sources close to the investigation said.

Rosas was responding to a report of smuggling activity near the rural town of Campo, about 60 miles east of San Diego, when he was attacked about 9 p.m. by one or more assailants.

There were signs of a struggle, and the attackers took Rosas' weapon, radio and other personal gear, according to the sources.

The detainees -- one or more of whom may have been injured in the confrontation -- are believed by Mexican authorities to have escaped over the border into a remote, largely lawless area overrun by bandits and smugglers.

Mexican authorities arrested four alleged smugglers who were escorting 21 immigrants through the area. One of those men identified Parra as the shooter, according to a news release from Mexico's secretary of public security.

The release also said authorities seized three rifles, a revolver and more than 100 rounds of ammunition.

It is unclear how the alleged immigrant smugglers are connected with Parra. He was arrested by Tecate police about 2 a.m. Friday morning with a gun tucked in his waistband, according to police.

In another possible lead, FBI officials have yet to say whether a man at a San Jose hospital is connected with the case. Homeland Security officials detained the man Friday afternoon at O'Connor Hospital there.