Appearing before the education select committee Zahawi acknowledged the financial challenges facing councils but said they should be able to support families and prevent children entering the care system through their existing resources. He said "throwing money" at the situation "doesn't work".
Figures published last September show that the number of children in care is rising at its fastest rate in five years. There were 72,670 children in care in the 12 months to the end of March 2017, compared with 70,440 the year before and 69,480 in 2015.
But Zahawi rejected suggestions that government spending on early support for families should be increased, instead arguing that the best way to reduce the children in care population was to spread evidence of schemes that are successfully doing this.
He said that the £20m What Works Centre for Children's Social Care which is expected to launch in 2020 and is tasked with promoting evidence-based practice, will be central to the government's approach.
"What we are doing is seeing what works, which is why we have set up the What Works Centre for Children's Social Care and the Innovation Programme, and spreading it. That's the best way," he said.
"The alternative is that I just sit here and say I'm going to throw money at this thing and everybody is going to be happy. It doesn't work. Trust me. I've seen what these families need and it is complex and difficult work."
Committee member Lucy Allen, who is Conservative MP for Telford, said councils are struggling to cope with increasing demand for children in care services and are being forced to reduce spending on early intervention.
"It is putting huge pressures on the system. It is putting huge pressures on budgets because the crisis end of spending has to take priority as it is a statutory intervention and it is diminishing available spend on early intervention," she said.
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Zahawi said that he believes that "good leadership" is another driver for improving support for families.
He cited Doncaster children's services, which moved from an "inadequate" rating from Ofsted to "good" under the leadership of an indepdendent children's trust, as an example of this.
"When I travel around the country and look at children's services, whether in Hackney, or Islington or Doncaster or Hampshire or Staffordshire what I see is that of course there are financial pressures on the system and it is important that I have a much sharper and clearer view on the financial challenges," he said.
"But what I also see, and the sector bears this out, is good leadership makes a huge difference.
"I asked the social workers in Doncaster who turned around that failing children's services with a spiral of failure. I got them in a room and got the leadership to leave the room.
"I said ‘70 per cent of you are the same people who were there when children's services were failing the children and families in Doncaster, what happened? What is the magic source that you introduced that allowed you to go from that spiral of failure to success'.
"To a man and a woman they said to me it was having a strong leadership that was consistently there for them and gave them the confidence and the support to deliver for those children and families."
Earlier this month Zahawi attended the Association of Directors of Children's Services annual conference when the organisation's president Stuart Gallimore said there was "no fat left to trim" in children's services due to a decade of government austerity measures combined with increasing demand.
Speaking after Gallimore, Zahawi said that he wanted to work with the sector "to understand the evidence for additional investment".
The Local Government Association has previously warned that annual spending by councils on children's services will increase by £2bn by 2020
Zahawi was appearing in front of the education committee as part of their regular accountability sessions with ministers.
During the session Zahawi also said he was committed to tackling schools that "off roll" or exclude children with special education needs.
"It is unacceptable for schools to off roll, it is illegal to unofficially exclude, and mustn't happen. Schools should work together to ensure there are no exclusions," he said.