David Bell was quizzed by the House of Commons education select committee this week about an internal survey which showed that one in five staff at Ofsted said they had been bullied and harassed.
The survey of 2,000 staff, first made public by The TES, found that two-thirds believed stress was damaging their work.
Mr Bell said that Ofsted was tackling the problems by encouraging the service to deal with bullying in the same way that inspectors would expect it to happen in schools.
But he said that job cuts could hinder progress. Ofsted has agreed to make more than 500 of its staff redundant, nearly a fifth of its workforce, and to accept a pound;40 million cut in its annual budget by 2008.
Mr Bell said this had potential to create "more stress, more anxiety, more pressure".
After meeting the MPs he said: "People are seeing that 500 jobs are going.
It doesn't make life any easier for any of us but it is not a reason to say we are going to give up."
The chief inspector said earlier that he accepted the need for cut-backs, which were part of a wider efficiency review being led by the Treasury.
A third of Department for Education and Skills staff are expected to go under the review and civil servants were striking today.
Mr Bell suggested that many staff had reported bullying because they had "been given an earful by members of the public". However, the survey attributed four-fifths of cases to Ofsted managers. Robert Green, director of corporate services for Ofsted, said the reasons behind many of the complaints were "encapsulated by what people call the 'target culture'.
People have found it hard to adjust to a situation where they have pretty clear things to do," he said.
Mr Green said that Ofsted was improving training for managers, urging staff to come forward in confidence, and assigning a team which will include educational psychologists to work on the bullying issues.
Asked about anti-bullying procedures in schools, Mr Green said: "We must apply internally the things we know about and apply externally."
MPs also quizzed Mr Bell about outdoor education, which is the subject of a separate investigation by the select committee.
The chief inspector criticised the National Association of Schoolmasters Union of Women Teachers for instructing its members not to take school trips.