The Obama administration was facing intense pressure on Monday to bring a federal prosecution against George Zimmerman, acquitted of murdering the unarmed black teenager Trayvon Martin, as activists called for a day of action to protest against the verdict.

Eric Holder, the US attorney general, said on Monday that he shared concerns about Martin's "tragic, unnecessary death", and promised that the Department of Justice would renew the federal investigation that it launched last year.

Civil rights leader the Rev Al Sharpton said vigils would be held in at least 100 cities across the US next Saturday. Zimmerman, meanwhile, could be back in court within a year if Martin's parents follow through with their intention to file a civil suit against him.

Benjamin Crump, a lawyer for the Martin family, said he would discuss the proposed lawsuit with them in the coming days as they continued to come to terms with Saturday's decision by the jury to acquit Zimmerman of murdering their 17-year-old son. The jurors accepted Zimmerman's contention that he acted in self defence.

Speaking in Washington, Holder said the Department of Justice would look carefully at the case. "The Justice Department shares your concern – I share your concern – and, as we first acknowledged last spring, we have opened an investigation into the matter," Holder told an audience of members of the Delta Sigma Theta sorority.

"We are resolved, as you are, to combat violence involving or directed at young people, to prevent future tragedies and to deal with the underlying attitudes, mistaken beliefs and stereotypes that serve as the basis for these too common incidents. And we will never stop working to ensure that — in every case, in every circumstance, and in every community — justice must be done."

The acquittal has placed Holder, the first black attorney general, and Obama, the first black president, in a difficult position. Civil rights campaigners are clamouring for a federal trial in the wake of the weekend acquittal, but the not guilty verdict has undermined the chances of any federal prosecution.

If Zimmerman is to face new charges under federal law, they would almost certainly be under the Hate Crimes Prevention Act, which was enacted by the Obama administration in 2009. Federal prosecutors would need to prove beyond reasonable doubt that Zimmerman, who is of white and Hispanic origin, wilfully inflicted bodily injury because Martin was black. If found guilty, he could face life imprisonment.

Although Holder is likely to review the a case as high-profile as this, the investigation will be led by the assistant attorney general for civil rights, Thomas Perez. Former Justice Department officials expressed doubt about the success of a federal prosecution on Monday.

"Racially motivated cases are very difficult because you need to establish the state of mind of the perpetrator at the time he committed the crime," said William Yeomans, who was acting assistant attorney general in 2001. "It would require showing that George Zimmerman was motivated by race in this instance."

Yeomans, who was also a chief of staff in the Justice Department, and is now a law professor in Washington, said government prosecutors would have "a very difficult hurdle" to overcome in the case. The department has also traditionally been cautious when bringing federal charges in cases that have already been tried at state level, he said.

Holder is likely to address the issue in more detail when he gives a speech about gun crime and race in Florida on Tuesday, less than 40 miles from where Martin was shot dead. Holder is speaking at an event organised by the National Association for the Advancement of Colored People, which has expressed outrage at the acquittal of Zimmerman.

Trayvon Martin supporters in Miami. Al Sharpton said vigils would be held in at least 100 US cities next Saturday. Photograph: Michael Marko/Demotix/Corbis

Martin's family were considering their options in the light of Saturday's verdict. Under Florida's statute of limitations, a civil suit for wrongful death must be filed before the second anniversary of Martin's death on 26 February next year. It carries a much lower burden of proof than the criminal charge, but faces the significant hurdle of the state's stand-your-ground law that allows for the use of deadly force if a person fears their life is in danger.

Jasmine Rand, another attorney representing Martin's parents, Sybrina Fulton and Tracy Martin, told the Guardian on Monday that they had not yet made a final decision. "I believe they will pursue it, but it's up to them. There are much larger issues at hand such as making sure this doesn't happen again," she said.

"They are heartbroken by the verdict but at the same time inspired by all the love and support they have received from within the nation and worldwide, and by President Obama's inspiring words yesterday."

Obama issued a statement calling on Americans "to respect the call for calm reflection from two parents who lost their young son" and urging citizens to "widen the circle of compassion and understanding in our own communities."

Mark O'Mara, Zimmerman's lead defence attorney, said: "If someone believes it's appropriate to sue George Zimmerman, then we will seek and we will get immunity in a civil hearing, and we'll see just how many lawsuits are spawned from this fiasco. We're not quite done yet."

In April, Martin's parents settled a $1m wrongful death claim against the homeowners' association of the Retreat at Twin Lakes development for an undisclosed sum. As part of the settlement, the association did not admit any liability and both sides agreed not to discuss it publicly.

Sharpton said on Monday that vigils would be held in at least 100 cities across the US on Saturday. "It's not over. And we are going to make sure it's not over, that's why we're calling people to organise in your city. I don't care if it's 20 people, we want to show the nation that over 100 cities a week later is still demanding justice," he said in a radio interview.

Zimmerman's wife Shellie, meanwhile, is likely to be the next member of the family to face court as the Florida state attorney's office pursues a charge of perjury against her. The case was postponed for the duration of her husband's criminal trial and will now be reactivated.

Prosecutors claim she lied to the court at her husband's bail hearing last summer when she said the couple was virtually penniless, despite having collected more than $150,000 in public donations from his website.