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Seven Held Over Sears Tower Plot
However, senior federal sources told CNN, "These people were not related to al Qaeda." When asked whether they were al Qaeda wannabes, he replied, "possibly."
Some sources also reported that some of the men had surveyed the buildings they allegedly were targeting and taken photos.
"We'll have more about that when the operation is completed, probably tomorrow morning," FBI Director Robert Mueller said in a taped statement for CNN's "Larry King Live."
One suspect was arrested before Thursday, officials said, and one of Thursday's arrests took place in Atlanta. (Watch details of the raids -- 2:53)
Federal sources said five of the seven men were Americans, one was an illegal alien from Haiti whose visa had expired and the last was a resident alien.
The 110-story Sears Tower in Chicago is the world's third-tallest building and the tallest in the United States. Investigators said other structures also may have been targets.
No weapons or bomb-making materials had been found so far in the raids, conducted in the Miami area, including a warehouse in a Liberty City housing project, law enforcement officials said.
No one was inside the warehouse, and it wasn't known exactly where police took the suspects into custody.
The neighborhood was cordoned off around the windowless warehouse about 2 p.m., and neighbors were told to stay inside. Police then showed neighbors photos of the suspects, who had been living in the building since March.
Neighbors said the men, who wore turbans, caused no problems but seemed odd.
"All you could do was just see their eyes. They had their whole head wrapped up. Just the eyes showing. And they were standing guard -- one here, one there -- like soldiers. Very quiet," one woman said.
A man said the men never spoke to neighbors and would just nod their heads if spoken to.
"They was acting like they was in military training," he said.
A spokeswoman for Miami-Dade Mayor Carlos Alvarez said the mayor was notified of the raid earlier in the day, and a spokesman for Gov. Jeb Bush said the governor had been notified Thursday morning. Both Alvarez and Bush said they had no plans to tighten security.
"If anything, this is a plot foiled," said Alvarez spokeswoman Vicki Mallette. Plans for a massive rally Friday for NBA champions the Miami Heat are unchanged, she said, adding that 200,000 people were expected to attend.
FBI spokesman Rich Kolko said there was at least one search warrant executed in the investigation.
"There have been several arrests. The documents in this case are currently sealed. There is no threat to Miami or any other area at this time. There will be more information tomorrow," Kolko said.
A law enforcement official told CNN the probe had been ongoing for at least four months.
Another statement was issued by the U.S. Attorney for Miami, Alex Acosta.
"Earlier today, the FBI, in conjunction with federal, state and local authorities, executed arrests as part of an ongoing investigation into a terrorist-related matter.
"The individuals arrested posed no immediate threat to our community. A press conference will be held in Washington, D.C., and in Miami on Friday to provide additional details," Acosta said.
A man who identified himself as "Brother Corey" said five of the men arrested in Miami were his "brothers," members of the group he identified as "Seas of David."
Brother Corey said the group has "soldiers in Chicago," but was peaceful and not associated with any terrorist organizations.
"This is a place where we worship and also have businesses, as a work site as a construction company we are trying to build up," he said, referring to the Liberty City warehouse where the raids took place.
He said the Seas of David is a religious group that blends the teachings of Christianity and Islam.
CNN's Susan Candiotti, John Zarrella, Jeanne Meserve, Mike Brooks and Kevin Bohn contributed to this report.