About 7,000 people have stopped making regular donations to Oxfam since it emerged some of its staff used prostitutes in Haiti, MPs have heard.
Oxfam boss Mark Goldring apologised to the International Development Committee for the damage done to people in Haiti and the wider efforts of aid workers.
He said 26 claims of sexual misconduct had been made since the scandal broke.
Save the Children's Kevin Watkins also gave evidence, saying his charity had investigated 53 allegations in 2016.
Mr Goldring and two other senior Oxfam executives faced an uncomfortable morning of questions from MPs about the sexual misconduct of the charity's workers in Haiti after the earthquake in 2010.
The urgent session, called by the committee in response to allegations appearing earlier this month in the Times newspaper, was marked by repeated apologies.
Oxfam, which has almost 10,000 staff working in more than 90 countries, has denied a cover-up but its handling of the scandal is being investigated by the Charity Commission.
Since the story broke, Mr Goldring, who became chief executive in 2013, said 26 reports of recent and historical incidents had been made by Oxfam workers - 16 of them outside the UK.
Of the scandal, he said: "I am sorry, we are sorry, for the damage Oxfam has done both to the people of Haiti but also to wider efforts for aid and development by possibly undermining public support."
He denied there had been a cover-up, saying Oxfam had been trying to deliver a huge programme with 500 staff, and his predecessors would have believed they were making the right decision at the time. "I don't defend that decision," he said.
Mr Goldring also said he was "deeply sorry" for his remarks in a Guardian interview in defence of Oxfam when he said the attacks on the charity were as if it had "murdered babies in their cots".
He told MPs that at the time of the original investigation, Oxfam issued a press release revealing its findings of "serious misconduct" involving bullying, intimidation and breaches of the charity's code of conduct - but did not mention sexual exploitation.
"At the time, people thought that was being transparent. We know now that that was not enough," said Mr Goldring.
"I suspect there was a balance of saying 'Oxfam is delivering life-saving assistance to a million people in Haiti. We have got to keep that work going'."
He added: "Not every organisation chooses to tell the public about something they got wrong."
He said there was now a safeguarding team and helpline at Oxfam and the charity was seeking more independent support.
Caroline Thomson, the chair of trustees since 2017, and Winnie Byanyima, executive director of Oxfam International, both told the committee they were "ashamed" of what happened in Haiti.
Ms Byanyima said the situation was "painful" as she has spent her life protecting women.
The number of lost donations referred to by Mr Goldring relates to direct debits. Oxfam confirmed later it had lost 7,094 direct debits - representing about 3.5% of the total number of donations received through that method.
Committee chairman Stephen Twigg said MPs would conduct a full inquiry into sexual misconduct in the aid sector.
Save the Children UK's chief executive Mr Watkins told the committee said his charity had produced two reports warning that "predatory men" were seeking to use aid work as an opportunity for abuse.
"What has come to light over the past few weeks cautions all of us against complacency," he said.
He said Save the Children has been pushing for an "international humanitarian passport", which could be revoked if aid workers breach rules.
Mr Watkins said of the 53 "safeguarding cases" it had investigated in 2016, 20 files had been passed to police and 11 staff members had been dismissed.
He added across Save The Children UK and International there were 35 cases of staff harassment reported and 19 staff dismissed.
'Bullying and intimidation'
A redacted version of an internal Oxfam report from 2011, released on Monday, revealed that three of the men accused of sexual misconduct in Haiti physically threatened witnesses during an investigation.
It also showed an employee was dismissed and three resigned for using prostitutes on Oxfam premises and the use of underage prostitutes was not ruled out.
During the committee hearing, it emerged that one of them was re-employed for Oxfam on a short-term contract in another country.
In the report, the charity said director of operations in Haiti, Roland Van Hauwermeiren, "admitted using prostitutes" at his Oxfam residence. Last week, he denied paying prostitutes for sex.
He was granted a "phased and dignified exit" and was allowed to resign, the report added, so long as he fully co-operated with the rest of the 2011 investigation.
It is not known if he was one of the suspects accused of threatening witnesses.