Sanford, Florida (CNN) -- A girl who overheard part of an incident involving Florida teenager Trayvon Martin can help prove he was killed "in cold blood" by George Zimmerman, a neighborhood watch volunteer, an attorney for Martin's family said Tuesday.
The girl, who was dating the 17-year-old, "completely blows Zimmerman's absurd self-defense claim out of the water," lawyer Benjamin Crump told reporters.
The girl -- who he said does not wish to be identified -- "connects the dots" about what happened that day when she lays out what she overheard while on the phone with him, he said.
Martin was fatally shot on February 26 while walking to the house of his father's fiancee in Sanford after a trip to a nearby convenience store. Zimmerman has acknowledged shooting Martin.
Speaking on the phone shortly before he was shot, Martin told the girl that someone was following him and that he was trying to get away, Crump said.
The girl said that, during the phone call, she heard someone ask Martin what he was doing and heard Martin ask why the person was following him, Crump said. The girl then got the impression that there was an altercation in which the earpiece fell out of Martin's ear and the connection went dead, Crump said.
Based on what she heard, the girl believes that Martin was pushed, said Crump, who added that the girl did not hear any gunfire.
Phone records show Martin was on the phone with her much of the day, including around the time of the killing, Crump said. He argued that if Martin were really "up to no good," he wouldn't have been chatting with his friend on the phone.
The girl said Martin was "his regular self," Crump said, arguing that any suggestions that the boy was "high" are "preposterous."
"It's what Zimmerman wants you to believe so he can justify killing this kid in cold blood," Crump said.
Natalie Jackson, another attorney for the Martin family, said police had not interviewed the girl.
Sanford Police Sgt. David Morgenstern said "at the onset, we asked any and all witnesses with information to come forward."
He would not say say whether the department has contacted the girl.
Morgenstern said Martin's cell phone was collected from the crime scene and investigators were working to acquire records associated with the phone's use.
The girl provided her account to Crump in a recording, which he said he will share with the Department of Justice, which is investigating.
Crump said the Martin family does not trust Sanford police to investigate.
Federal prosecutors and the FBI will investigate the incident, which has sparked claims of racial profiling and widespread calls for charges to be filed against Zimmerman.
Rep. Corrine Brown, D-Florida, Sanford Mayor Jeff Triplett and Sanford City Manager Norton Bonaparte met Tuesday with Justice Department officials: Assistant Attorney General for the Civil Rights Division Thomas E. Perez and Deputy Assistant Attorney General Roy L. Austin Jr.
"The gentlemen we spoke with -- they said they will not only look at what we've done, but they will also ... I think his exact comment was there will be no stone that won't be overturned," Triplett said.
A grand jury will also help investigate the death of the unarmed African-American teenager.
A police report describes Zimmerman as a white male; his family said he's a Spanish-speaking minority.
The Seminole County Grand Jury will convene April 10, State Attorney Norm Wolfinger said in a statement.
Gov. Rick Scott, who is asking the Florida Department of Law Enforcement to provide "any assistance necessary" to local investigators, insisted Tuesday he would work to ensure "justice prevails."
The governor met Tuesday in Tallahassee with criminal defense lawyers and protesters who said his office should be more involved and form a task force on racial profiling.
But Scott said any such task force shouldn't be formed until after a formal investigation. "There should not be racial profiling anywhere," he told the group.
Florida Attorney General Pam Bondi said she was "devastated and deeply troubled" over the killing. "When someone loses his life at the hands of another, there cannot be any questions surrounding the circumstances of the death," she said in a statement.
She said she had spoken with FDLE Commissioner Gerald M. Bailey, "and I know that a complete and thorough review of the facts will be conducted."
She added that while it is up to the Seminole County State Attorney's Office to decide whether to file charges, "I will remain vigilant in ensuring that questions are answered."
Police say they have not charged Zimmerman, 28, because they have no evidence to contradict his story that he shot in self-defense.
In a police report, Officer Timothy Smith says that, when he arrived at the scene of the shooting, a black male was laying face down on the ground, his hands underneath his body. "I attempted to get a response from the black male, but was met with negative results," the report says.
After speaking with Zimmerman, who had called 911, Smith observed that Zimmerman's "back appeared to be wet and was covered in grass, as if he had been laying on his back on the ground. Zimmerman was also bleeding from the nose and back of his head."
Smith wrote that Zimmerman stated, "I was yelling for someone to help me, but no one would help me." Martin's family insists it was Trayvon Martin who was heard yelling for help.
Three witnesses who were nearby have said it was Martin who was heard screaming for help in the 911 call placed by Zimmerman, Crump said.
Martin's father said the family believes race was a factor in their son's death, fueling public outcry over the incident in the racially mixed community 16 miles northeast of Orlando.
"I think that's an issue that Mr. Zimmerman himself considers -- as someone suspicious -- a black kid with a hoodie on, jeans, tennis shoes," Tracy Martin, the teenager's father, told CNN. "Thousands of people wear that outfit every day, so what was so suspicious about Trayvon that Zimmerman felt as though he had to confront him?"
Zimmerman's family has denied race played any role. Zimmerman has "many black family members and friends. He would be the last to discriminate for any reason whatsoever," his father, Robert Zimmerman, said in a statement to the Orlando Sentinel.
The case was one of the most-discussed topics Tuesday morning on Twitter, much of it dedicated to an online petition posted by Trayvon's parents calling on Florida authorities to charge Zimmerman.
As of Tuesday evening, more than 638,000 people had signed the petition at Change.org, making it one of the site's largest petition campaigns ever, spokeswoman Megan Lubin said. More than 10,000 people an hour were signing the petition early Tuesday.
Demonstrators who have turned out in recent days to protest police handling of the case have mocked Zimmerman's claim, carrying bags of Skittles like the one Trayvon had bought shortly before his death.
CNN has made numerous attempts to contact Zimmerman but has been unsuccessful.
Zimmerman has moved out of his home after receiving death threats, his father said.
Florida's deadly force law, also called "stand your ground," allows people to meet "force with force" if they believe they or someone else is in danger of being seriously harmed by an assailant, but exactly what happened in the moments leading up to Trayvon's death remains unclear.
In his statement last week, Zimmerman's father said his son never followed or confronted Trayvon. But on Monday, police released 911 recordings in which Zimmerman says he is, in fact, following the boy.
"Something's wrong with him. Yep. He's coming to check me out," Zimmerman tells a police dispatcher. "He's got something in his hands. I don't know what his deal is. Send officers over here."
The teen started to run, Zimmerman reported. When he said he was following, the dispatcher told him, "We don't need you to do that."
Minutes later, someone who lives near the scene of the shooting called 911 to report an altercation. In the background, someone can be heard screaming for help, but the caller said she was too afraid to go outside and see what was going on.
"It's heart-wrenching, because those actually were my son's last words," said Trayvon's father. "And to hear his last words being cries of help, is devastating. It tears me apart as a father."
The state attorney's office also said a voice analysis would be conducted on 911 calls from the night of the shooting to determine who was yelling for help.
Florida Rep. Dennis Baxley, who was the prime House sponsor of the deadly force legislation, told CNN Tuesday that "nothing in 'stand your ground' authorizes (you) to pursue and confront."
White House spokesman Jay Carney said Monday that the FBI was monitoring the case but that the White House was not going to "wade into a local law enforcement matter."
The Congressional Black Caucus, the Congressional Hispanic Caucus, the Congressional Asian Pacific American Caucus and the Congressional Progressive Caucus have also called for a federal investigation, with the Black Caucus saying Sanford police showed "blatant disregard for justice."
CNN's Josh Levs, Sunny Hostin, Vivian Kuo, Roland S. Martin, David Mattingly, Rick Martin, John Couwels, Phil Gast and Terry Frieden contributed to this report.