Chief executive Mark Goldring told a parliamentary committee in London that the cases varied in their seriousness, while 16 related to its international operation.
“They range in time frame from more recent events to long historic events where people did not report them at the time,” he said.
Goldring added he believed the latest cases had emerged as “a direct response to the publicity” around the Haitian scandal.
“We really want people to come forward,” he added.
The Oxfam chief was unable to provide further details on the cases when pressed by British lawmakers.
The committee said it would be conducting its own inquiry into abuses in the foreign aid sector.
Three of Oxfam’s most senior leaders repeatedly apologized for the charity’s handling of an internal investigation into the use of prostitutes by staff in Haiti following the devastating 2010 earthquake.
Caroline Thomson, chair of trustees, said: “It’s right to admit this has been a real wake-up call.”
The charity revealed 7,000 regular donors had been lost since the scandal emerged following reporting by The Times newspaper.
It said safeguards had been put in place following the 2011 probe, but admitted they had not gone far enough.
Thomson vowed to take “personal responsibility” for ongoing reform: “I have decided that we need to have more focus on safeguarding.”
Last week, Oxfam unveiled an action plan to tackle sexual harassment and abuse, including creating a new vetting system for staff.
The charity formally also apologized to Haiti on Monday over the scandal and for failing to report the matter adequately.
“Oxfam should have reported the matter to the Haitian authorities,” Goldring told lawmakers.
“It was not for Oxfam to decide whether a crime had been committed ... that was the wrong decision.”