Political pressure on Rupert Murdoch has spilled across the Atlantic with a growing number of senior politicians calling for a legal investigation into whether News Corporation broke American laws over the phone-hacking scandal.

Members of Congress from both major parties have waded in to the affair with warnings of "severe" consequences if a report in the Daily Mirror that the News of the World attempted to access the voicemails of victims of the 9/11 terrorist attacks or other Americans is true.

Two New York members of the US House of Representatives, Pete King and Louise Slaughter, demanded an immediate justice department investigation of whether US laws were broken, particularly in relation to any attempt to hack in to the phones of terrorist victims.

King, who is the Republican chairman of the House homeland security committee, said in a letter to the FBI director, Robert Mueller, that journalists should face felony charges if evidence is found.

"The 9/11 families have suffered egregiously, but unfortunately they remain vulnerable against such unjustifiable parasitic strains. We can spare no effort or expense in continuing our support for them," he said in the letter.

Slaughter called for the application of the "full force of the law".

Four Democratic senators have joined the demands for an investigation of whether US anti-graft laws were broken by News Corporation as well as the alleged hacking of Americans' phones.

The calls for an inquiry were backed by family members of people who died in the World Trade Centre. "Someone should look into it to see if their rights were violated – the family members I've talked to are appalled, they're disgruntled, they have to relive the pain all over again," Jim Riches, a former deputy chief in the New York fire department whose son died in the 9/11 attacks, told Politico: "I think they crossed the line. They're trying to get messages from loved ones in the last moments of their lives. It's horrible, and they should be held accountable."

The Guardian has so far been unable to verify the Daily Mirror story.

Rosemary Cain, who lost her firefighter son George, said that she did not know whether the Mirror report was correct or a foul rumour, but she wanted an investigation to ascertain the truth. "If it did turn out to be true it would be a despicable invasion of privacy and something that should be prosecuted to the fullest extent."

Sally Regenhard, whose son also died as a firefighter on 9/11, said she'd heard the Mirror story on local media in New York and wanted to know what had really happened. "I'm very concerned about the privacy of citizens whether it's in this country or others. If there's any suggestion that a paper had hacked into 9/11 victims' phone calls, that should be investigated."

The calls for an investigation come as Murdoch faces pressure from a group of American shareholders, including pension funds and banks, who have taken legal action saying it is "inconceivable" that the News Corp's board was unaware of the phone hacking and other illicit practices, and accusing him of using the company for "personal and political objectives".

Senator Frank Lautenberg has asked the securities and exchange commission and the justice department to investigate whether US laws against the payment of bribes abroad were broken by Murdoch's parent company.

In a letter to the attorney general, Eric Holder, Lautenberg said allegations that NoW journalists bribed UK police officers are potentially a breach of the US's Foreign Corrupt Practices Act which bars American companies from paying bribes abroad.

"The limited information already reported in this case raises serious questions about the legality of the conduct of News Corporation and its subsidiaries under the FCPA," the Democratic senator wrote. "Further investigation may reveal that current reports only scratch the surface of the problem at News Corporation."

Another senator, Jay Rockefeller – chairman of the commerce, science and transportation committee – has described the activities of Murdoch's newspapers in Britain as "offensive" and called for an investigation into whether Americans had their privacy invaded.

"I am concerned that the admitted phone hacking in London by the News Corporation may have extended to 9/11 victims or other Americans. If they did, the consequences will be severe," he said.

Senators Robert Menendez and Barbara Boxer have also publicly called for a justice department probe.

An investigation could threaten some of the most profitable parts of Murdoch's empire, including his TV networks that cover nearly half of the US and are licensed by the Federal Communications Commission which has the power to revoke licences over criminal convictions.

Murdoch, who became an US citizen in 1985, may also have personal legal responsibility.

Rockefeller's statement came in response to a letter from Citizens for Responsibility and Ethics in Washington (Crew) to the heads of four congressional committees appealing for the legislature to investigate whether Murdoch's papers in the UK or the US were involved in illegal actions against American citizens.

Melanie Sloan, executive director of Crew, described Rockefeller's comments as "heartening". She said that while there is not yet the same clamour for an investigation in the US as there is in Britain that could rapidly change if it is revealed that Americans were the target of illegal practices, particularly the victims of terrorist attacks.

"It's a pretty serious allegation for people in America. There's few people who get more respect and deference in America than 9/11 victims and their families," she said.

Most of the politicians leading the calls for an investigation are Democrats, whose party is regularly attacked by Murdoch-owned Fox News and his newspapers in New York.

"I think Murdoch is vulnerable in America because he's made so many enemies," said Sloan.

"By the same token he's still very powerful and I don't think you're going to see members of Congress rushing to take on somebody who's got Fox News, even liberals. They don't need Fox News railing against them on other issues. But on the other hand if it becomes a choice between supporting Murdoch or American citizens who've had their phones tapped, the calculus would change dramatically."

The Centre for American Progress Action Fund, headed by Bill Clinton's former chief of staff, John Podesta, is collecting signatures for a letter to the justice department demanding an investigation.

"Given the seriousness of these allegations, we ask that you immediately begin an investigation of all entities controlled by News Corp, including domestic subsidiaries such as Fox News, The Wall Street Journal, and the New York Post," it says.