Pressure on Florida police to make arrest after Martin's girlfriend tells how she heard teen walking away from George Zimmerman

Florida police are under mounting pressure to arrest self-appointed neighbourhood watch volunteer who shot dead an unarmed teenager following dramatic new evidence from the victim's girlfriend.

The family of Trayvon Martin, 17, say the account from his girlfriend completely contradicts his killer's self-defence claim.

In a dramatic press conference on Tuesday, the Martin family's lawyer Benjamin Crump detailed how the unnamed girl – a minor who was so traumatised by Martin's death she was taken to hospital at his wake – was talking to him on his cell phone in the minutes leading up to his death, and heard the altercation with his killer.

Trayvon Martin. Photograph: AP

Martin, 17, was shot by Hispanic volunteer watch captain George Zimmerman, who spotted the teenager while patrolling the neighbourhood on a rainy evening in February. Zimmerman, 28, claims he shot the teenager with his licensed 9mm handgun in self-defence during a confrontation.

The failure of local police to arrest Zimmerman in the three weeks since the shooting – and the release of 911 tapes that reveal he followed Martin, despite a warning by a police dispatcher not to – has fuelled a fierce debate on race, vigilante justice and a "stand your ground" law in Florida that allows people to defend themselves using deadly force.

Crump said that during the final phone call with his girlfriend, who was back home in Miami, Martin told her that a stranger was following him, according to an affidavit she recorded. Martin had then tried unsuccessfully to get away from the stranger.

"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 then heard Martin saying "Why are you following me" and another voice saying "What are you doing here?" She told Crump they both repeated themselves, and then she thinks she heard Zimmerman push Martin "because his voice changes, like something interrupted his speech." She heard an altercation and then the phone call was cut off, Crump said.

When police arrived a minute later, at 7.17pm, Martin was lying dead in the street.

There are about 22,000 registered neighbourhood watch groups worldwide and Zimmerman was not part of a registered group which police were aware of, Chris Tutko, the director of the National Neighborhood Watch told ABC News. Had he been, he would have violated parts of the manual which states: "It should be emphasized to members that they do not possess police powers. And they shall not carry weapons or pursue vehicles."

Before the phone call emerged, there were no witnesses to what happened immediately before the killing, which took place as Martin returned from the local store to the home of his father's girlfriend in a gated community in Sanford, near Orlando.

But now, Crump told reporters, the girl's evidence "connected the dots" on the killing. Phone logs also showed that Martin had been on the phone to the girl throughout his trip to the local store to buy candy and drink, he said, disproving Zimmerman's claim that Martin had been acting suspiciously.

"This claim that Trayvon Martin was the aggressor is preposterous, and it can't be allowed to stand" said Crump. "The dots have all been connected. Arrest George Zimmerman. Arrest him today."

George Zimmerman. Photograph: AP

Local police say they did not arrest Zimmerman because there were no witnesses to challenge Zimmerman's claim that he acted in self-defence.

Crump told reporters: "He was just a kid trying to get home from the store and trying to get out of the rain."

Details of the girl's evidence came after the US justice department responded to the national outcry over case by announcing it was launching an investigation into the killing, along with the FBI. Florida authorities also announced on Tuesday that a grand jury would hear evidence about the shooting next month.

"The public is entitled to no less than a thorough, deliberate and just review of the facts," state attorney Norm Wolfinger said. "We intend to honor that commitment."

The investigations follow a national outcry over Martin's death, which has seen almost 500,000 people sign a petition on the change.org website calling for Zimmerman to be prosecuted.