Earlier this week, Oxfam Deputy Chief Executive Penny Lawrence resigned over the scandal, saying she was "deeply sad" and "took full responsibility" for purported misconduct by staff in Chad and Haiti.
"I'm appointing a high-level, independent commission that will look into our culture and our practices and make recommendations to make us stronger at protecting our people", she told the BBC.
I am inviting anyone who has been a victim of abuse to come forward.
The International Development Secretary said Oxfam had a "long way to go to regain the trust of the British public".
Haiti's president told Reuters on Friday that sexual misconduct by Oxfam staff was only the tip of an "iceberg" and called for investigations into Medecins Sans Frontieres (Doctors Without Borders) and other aid organisations that came to the country after a devastating quake in 2010.
In an interview with the BBC's diplomatic correspondent James Landale, she switched to speaking in a Ugandan language to make an apology: "From the bottom of my heart forgive us, forgive Oxfam".
Van Hauwermeiren, who left Oxfam in 2011 amid a sexual misconduct inquiry, has denied hiring prostitutes but said he had "intimate relations" with a woman who was "not a prostitute".
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"I think that these people should be considered persona non grata", she said of the charity, which spent $15 million on its operations in the country past year and employs 248 staff.
In comments to reporters at the newspaper Het Nieuwsblad, who tracked him down in an unidentified town on the Belgian coast, Van Hauwermeiren said there were "lots of lies and exaggerations" in media reports.
The government has made three demands of Oxfam: that it produce a plan on how to deal with any forthcoming allegations, that it report any staff members involved in the Haiti scandal and that it fully cooperate with the Haitian authorities.
Oxfam said its decision to rehire the man in Ethiopia was a "serious error".
The charity on Friday said it was also investigating allegations of sexual misconduct at a hotel in the Philippines after a destructive typhoon in 2013.
The charity is also introducing a number of immediate measures - including creating a new global database of accredited referees to combat "unreliable" references by past or current staff, and extra resources for the charity's safeguarding processes.
Ms Mordaunt said: 'We will not work with any organisation that does not live up to the high standards on safeguarding and protection that we require.