Rupert Murdoch faces a growing legal challenge in the heart of his global media empire as lawyers representing alleged victims of phone hacking on US soil begin gathering evidence ahead of possible court action.

Mark Lewis, the English lawyer who has been a driving force behind phone-hacking revelations in the UK, and his American legal partner Norman Siegel, have revealed that they have been approached by at least 10 people bearing complaints relating to Murdoch's News Corporation.

The complaints relate largely to alleged hacking by News of the World journalists into phones in the US, but also extend to other News Corp holdings including Fox News.

Lewis said that he had been contacted by a number of people since he arrived in the US last weekend "raising issues against other [News Corp] titles or Fox News, not necessarily about hacking but about other untoward dark arts to obtain information that should be private." He added that the new complaints were unproven allegations.

Lewis told reporters that he had taken on a fourth case of alleged phone hacking in the US. Previously, it had been known that he was representing three individuals, one of whom is an American citizen and two of whom are Europeans who believe their phones were hacked while visiting America.

In addition, Siegel, a former head of the New York Civil Liberties Union, said he had been contacted by six individuals raising complaints about News Corp outlets. "My experience in these sorts of cases is that when people sense you are serious and balanced in your approach, they begin to come out of the woodwork," he said.

The lawyers are refusing to name the four firm cases of alleged phone hacking inside America they are pursuing, saying that to identify them would be to further breach their privacy. So far all that is known of the original three is that one is a soccer figure, another from Hollywood and a third an American.

Lewis and Siegel said they had begun to compile evidence relating to the cases, and lawsuits could flow when they were ready. At the heart of the three initial cases are notes kept by Glenn Mulcaire, the private detective used by News of the World to carry out illegal hacking of the phones of potentially thousands of people.

Lewis claimed he had "substantial and substantiated" evidence relating to Mulcaire's notes that pointed to phone hacking on US soil between the years 2001 and 2006.

News Corporation said only that they had "no comment" on Lewis's American visit, but the stakes are potentially very high for the company. Both federal and individual state law takes a severe view of alleged hacking into a person's stored communications.

Under federal law, an individual who violates telecoms privacy for the purposes of commercial advantage can face five years in prison, or 10 years for a subsequent offence. Civil courts can also set damages measured against the profits gained by the violators.

Punitive damages can be imposed on any person or company found guilty of "wilful or intentional" violations of the law.

The new legal challenges may have particularly serious implications for James Murdoch, Rupert's youngest son, who recently relocated to New York from London, where he was chairman of the beleaguered UK newspaper group News International. Lewis indicated that he was exploring the possibility of deposing the younger Murdoch should any of the cases come to court.

"James Murdoch is now in the US rather than in England, and we have to look at that," Lewis said. "It becomes relevant to all sorts of issues in respect to knowledge in terms of punitive damages."

Asked whether Rupert Murdoch might also be deposed, he replied: "You go whereever the evidence takes you. We don't rule anything in or out."

Both Murdochs have been called to give evidence at the Leveson inquiry into phone hacking and media ethics in London next week.