The cases span 26 charities and groups and cover the ‘full spectrum’ of safeguarding incidents, the International Development Secretary and Portsmouth North MP said.
Seven of the organisations came forward with cases that have been reported within the current financial year.
Officials said they did not know if any of the incidents involved children and refused to name the charities involved.
Ms Mordaunt said it was a ‘wake up call’ for the sector, which has been reeling since the Oxfam sex scandal erupted.
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Speaking at a safeguarding summit in central London, the Cabinet minister warned predators exploiting the aid sector there is ‘no hiding place’.
‘We will find you, we will bring you to justice. Your time is up’, she said.
Ms Mordaunt wrote to 179 aid charities and organisations after it emerged there were widespread concerns about the behaviour of aid workers and the way they were being dealt with.
All have responded and given statements of assurance about the way they operate, but 37 still have questions to answer, the summit heard.
The Department for International Development has also carried out an internal audit and the findings are expected to be released on Monday.
New standards have now come into force that aid organisations must meet to be eligible for Government money, Ms Mordaunt said.
‘These standards will include an assessment of codes of conduct, how organisations identify and respond to incidents, and how their risk management places safeguarding and beneficiaries at the very core.
‘That assessment will set the bar at a level of the very best - a bar that we will continue to push higher - from our work here today and in the time to come.
‘Our standards will be world-leading. They will be tough and exacting.
‘Organisations should not bid for new funding unless they are prepared to meet these tough new standards. We will not approve funds to them unless they pass our new standards.’
NGOs and charities at the summit will sign a joint statement setting out the key principles they will follow and the action they will take next to restore trust in the sector.