Alex Salmond told MSPs there was "no doubt" that inspection and reinspection had improved the situation of child protection across Scotland during first minister's questions, on 17 May.
The first minister was responding to an appeal from Johann Lamont for a "full independent public inquiry" into child protect across Scotland, following a report into the role of social workers and health care staff in the case of murdered toddler Declan Hainey.
Drug addict Kimberley Hainey, 37, was sentenced to a minimum of 15 years for killing her son at their Paisley home.
Renfrewshire Council and the NHS commissioned a significant case review after his body was found in 2010.
The Scottish Labour leader called for a public inquiry into child protection after highlighting serious failures in the inspection regime.
It had been revealed that child protection services at Renfrewshire Council were found to be 'excellent' by inspectors - despite two case reviews which found 'systemic failures', including in the case of Declan Hainey.
Ms Lamont asked the first minister had Renfrewshire Council been" best placed to investigate itself?".
The first minister said the responsibility for the tragedies was with the perpetrator, adding individual social workers were accountable but not responsible and it was important to support social worker and department, to ensure there was "no complacency, constant vigilance and continuous improvement".
Scottish Conservative leader Ruth Davidson asked the first minister "was he hacked", saying Mr Salmond was "accountable to this chamber and the people of Scotland" who he was "currently holding in contempt" by not replying.
Mr Salmond said he was "happy" to go to the Leveson inquiry and give a "full account of my actions" and added he would be in substantially less trouble than certain member's of Ms Davidson's party.
Liberal Democrat MSP Liam McArthur asked the first minister what support there was for families looking after disabled foster children.
The first minister said the government was committed to promoting and reforming foster care, especially for those children who had special needs.
SNP MSP Sandra White asked the first minister if he could ask the BBC Trust to review its decision on the "job cutting exercise Delivering Quality First" given the "very grave concerns expressed about the potential impact of these cuts in Scotland".
The first minister said yes and he was concerned over the job cuts, "during a particularly important time in Scotland's history" and added he hoped "something of these damaging cuts" would be reversed.