Paul Lakin apologised again for what happened in the town at the beginning of a packed meeting of the council's ruling Labour cabinet. He said: "We have all been appalled by the terrible contents of this report.
"It is with a deep sense of regret that we are here today to discuss how, in the past as a council, we badly let down young people and families we were here to protect."
Last week's report by Professor Alexis Jay, a former Chief Social Work Adviser in the Scottish Government, outlined details of exploitation over a 16-year period with examples of girls who were raped, trafficked, threatened with violence and ignored by the statutory authorities.
The Jay Report sparked a wave of criticism of police, councillors and local authority officials but only council leader Roger Stone has resigned in its wake.
Home Secretary Theresa May told MPs on Tuesday that Communities Secretary Eric Pickles is "minded" to commission an independent investigation into Rotherham Borough Council following concerns of "inadequate scrutiny by councillors, institutionalised political correctness and covering up of information and the failure to take action against gross misconduct".
The council was under Labour control through the period in question, and the party has now suspended the authority's former leader, Mr Stone, and ex-deputy leader, Jahangir Akhtar, as well as serving councillors Gwendoline Ann Russell and Shaukat Ali, a former mayor.
A report prepared for the meeting yesterday by council chief executive Martin Kimber said: "The Jay Report is critical of past actions in a number of areas, but at the core is poor political and managerial leadership.
"The report indicates 'By 2005 it is hard to believe that any senior officers or members, from the leader and chief executive downwards, were not aware of the issue'.
"It is clear from the report that at this time some senior officers responsible for safeguarding simply did not do their jobs effectively."