London Metropolitan Police Deputy Assistant Commissioner Sue Akers, who is leading the investigation, expressed confidence police would investigate the allegations thoroughly and with sensitivity, The Daily Telegraph reported Thursday.
"I understand that many people may be upset and will want to seek information from us," Akers said. "I ask them to be patient and reassure them we will contact them if they are affected -- have confidence in us to keep our promise but also realize it will take time."
The number of victims of the British tabloid phone hacking could top 4,000, investigators warn.
Revelation of the Sunday tabloid's hacking activities -- especially news that it may have hacked phone accounts of families of military personnel who died in Iraq and Afghanistan -- drew widespread condemnation and the announcement by News International it was ending operations of News of the World.
Deputy Chief Operating Officer James Murdoch, chairman Rupert Murdoch's son and heir-apparent, said the newspaper would close because the allegations, if true, were "inhuman" and had no place in the company.
Officials expressed concern that the privacy invasion could extend to e-mails as well as telephone calls, the Telegraph reported.
More high-profile figures have said they were targeted illegally by the newspaper. Michael Mansfield, who represented the family of Dodi Fayed at the inquest into the death of Diana, princess of Wales, said police confirmed he was on a list of possible targets.
Akers said she has "huge sympathy" for the victims.
"It must be incredibly distressing to see details of the information held, or speculation about what may be held, about them in the media," she said. "This is forcing them to relive devastating experiences."