A Downing Street spokesman added: "We want to see Oxfam provide all the evidence they hold of the events to the Charity Commission for full and urgent investigation of these allegations".
Sex workers were reportedly invited to the Oxfam team house on a number of occasions.
Oxfam said it was "shocked and dismayed" by the new Chad claims although it said it could not corroborate the claims.
Caroline Thompson, who chairs Oxfam Great Britain's board of trustees, said charities that work in "fragile and unstable environments can become targets for abusers", but that the organization is committed to fixing the problems it faces.
Oxfam workers were accused of paying Haitian natural disaster survivors for sex during relief efforts.
MORE than 120 workers for Britain's leading charities were accused of sexual abuse in 2017 alone, it was revealed last night.
Oxfam lied and failed in its "moral leadership" in the wake of allegations of sexual misconduct by aid workers, the International Development Secretary has said. It said significant improvements had been made since 2011.
Caroline Thomson, Oxfam's chairwoman of trustees in the United Kingdom, said it was working to "address the underlying cultural issues that allowed this behaviour to happen".
When it happened, she said, new whistle-blowing procedures, safeguarding practises and training were put in place.
Oxfam Chief Executive Mark Goldring yesterday said it receives less than 10% of its funding from DFID and hoped to continue working with the department while rebuilding trust with the public.More news: Team USA Announces Its Flag Bearer: Luger Erin Hamlin
"Everybody, the 25,000 staff and volunteers are compromised by this".
Oxfam, one of the world's most prominent relief agencies, could lose its funding from the British government over reports that its workers exploited survivors of a massive quake in Haiti, and possibly other disasters, for sex.
The charity made a decision to allow Mr Van Hauwermeiren to step down from his position and crucially didn't share details of the termination of contract with his new employer.
Ms Mordaunt said the charity had also "categorically" stated to the DfID that beneficiaries were not involved in the misconduct and no harm was done.
"They still have information they should be giving to the authorities", she told the BBC's Andrew Marr show.
Mordaunt expected charities to "co-operate fully with. authorities, and we will cease to fund any organisation that does not".
Responding to a report in The Times newspaper, Oxfam admitted that the behaviour of some of its staff had been "totally unacceptable". Asked if that was a lie, Mordaunt said: "Well, quite".
However, the minister said Oxfam did "absolutely the wrong thing" by not reporting the detail of the incidents to the government.
In a further warning, she said: "If they do not hand over all the information that they have from their investigation and subsequently to the relevant authorities, including the Charity Commission and prosecuting authorities, then I can not work with them any more as an aid delivery partner".