Updated at 1:13 p.m. ET
(CBS/AP) SANFORD, Fla. - Federal and local prosecutors are launching parallel investigations into the fatal shooting of an unarmed black teen by a neighborhood watch captain as outrage over the case grows.
A central Florida prosecutor's announcement Tuesday that a grand jury will consider evidence in the case came a day after the Justice Department said it would probe the death of 17-year-old Trayvon Martin. The moves follow a day of protests calling for the arrest of George Zimmerman, 28, who claims he shot Martin in self-defense during a confrontation last month in a gated community in Sanford, Fla.
A source very close to the investigation told CBS News that Sanford police were under mounting political pressure from the city and the state to submit their case to the state's attorney before they were confident their part of the investigation was complete. Prosecutors will need to re-interview key witnesses.
The source provided additional details about Zimmerman's self-defense claim that he made to police.
Zimmerman spotted Martin as he was patrolling his neighborhood on a rainy evening and called 911 to report a suspicious person. Against the advice of the 911 dispatcher, Zimmerman then followed Martin, who was walking home from a convenience store with a bag of Skittles in his pocket. Police have described Zimmerman as white; his family says he is Hispanic and not racist.
While under questioning, Zimmerman told police he followed the dispatcher's advice and that he turned and began to return to his car when Martin confronted him, according to the source close to the investigation. Martin became violent and punched Zimmerman, he told police. The two got into a scuffle, during which Zimmerman drew his weapon and fired it, he told police.
On Tuesday, attorney Benjamin Crump, who represents Martin's parents, said the teenager was on the phone with his girlfriend back home in Miami when he told her he was being followed. She said Martinand that he was going to try to lose him. He thought he had lost Zimmerman but hadn't.
"He says, 'Oh he's right behind me, he's right behind me again,'" Crump said the girl told him. "She says run. He says I'm not going to run I'm just going to walk fast. She hears Trayvon say, 'Why are you following me?' Other voice says, 'What are you doing around here?'"
She told Crump they both repeated themselves and then she heard a scuffle begin "because (Martin's) voice changes like something interrupted his speech." She heard an altercation and then the phone call was cut off.
Within moments, according to Crump's timeline, Martin was shot. She didn't hear the gunfire.
Crump is not releasing the girl's name to protect her privacy.
According to the source close to the investigation, authorities have a subpoena for Martin's phone records and are waiting to electronically unlock the phone. Neither the teenage girl nor her parents came forward to offer details to police in the three weeks since the shooting, despite a public plea for information, the source said.
Several investigators don't believe Zimmerman turned back to his car but instead tried to confront or even detain Martin until police arrived, the source said, but police don't have any evidence to prove that. Police conducted a voice stress test two days after the shooting on Zimmerman, which he passed, the source said. Another one is expected to be conducted on him soon, the source said.
Zimmerman is staying at a secure location and has been in daily contact with authorities, the source said.
Crump said he plans to turn over information about the call to federal investigators who are looking into the case.
"The department will conduct a thorough and independent review of all the evidence and take appropriate action at the conclusion of the investigation," the Justice Department said in an emailed statement.
The federal agency said it is sending its community relations service this week to Sanford to meet with authorities, community officials and civil rights leaders "to address tension in the community."
In a statement released Tuesday, Seminole County State Attorney Norm Wolfinger urged the public to be patient as the investigation unfolds. He said grand jurors will meet April 10.
An online petition urging local authorities to prosecute Zimmerman has drawn more than 500,000 signatures at website Change.org
Civil rights activist Al Sharpton is expected to join Sanford city leaders in a Tuesday evening town hall meeting to discuss with residents how the investigation is being handled. Earlier Monday, students held rallies on the campus of Florida A&M University in Tallahassee and outside the Seminole County Criminal Justice Center, where prosecutors are reviewing the case to determine if charges should be filed.
Yet authorities may be hamstrung by a state law that allows people to defend themselves with deadly force.
Prosecutors may not be able to charge Zimmerman because of changes to state law in 2005. Under the old law, people could use deadly force in self-defense only if they had tried to run away or otherwise avoid the danger.