Speaking in Parliament this week, Zahawi said the government had no plans to look at introducing a national minimum allowance, despite figures earlier this year showing a fall in the proportion of young people moving from foster care to a Staying Put placement when they turn 18.
He was responding to a parliamentary question from Labour MP Alex Cunningham about whether the government planned to review Staying Put, including the "potential merits" of a national minimum allowance.
Cunningham, MP for Stockton North, raised the question after research by The Fostering Network published last month showed a quarter of foster carers cited inadequate allowances offered by councils as the main reason they were unable to offer a Staying Put placement.
Zahawi said that the policy is "under constant review", but rejected calls for a minimum allowance.
"The government does not believe that introducing a national minimum allowance for Staying Put carers is the right way forward. Unlike children in foster care, young people in Staying Put arrangements are adults and may be in work or claiming benefits," said Zahawi.
"These can be used to contribute to the cost of providing the Staying Put arrangement, in a similar way that young people who are still living at home with their parents may contribute to the cost of running the household."
Under the Staying Put initiative, which was made law through the Children and Families Act 2014, councils have a duty to support looked-after children who want to remain with their foster carer until they are 21.
Earlier this year, The Fostering Network criticised government progress on ensuring more looked-after children benefit from the policy after Ofsted figures published in April show the proportion of eligible young people in Staying Put arrangements fell from 54 per cent in 2015/16 to 46 per cent in 2016/17.
The Fostering Network has also criticised the government's national implementation adviser for care leavers Mark Riddell for paying too little attention to Staying Put in his first annual report published earlier this month.
Riddell's report gives a brief mention to the arrangements as a way of ensuring care leavers can feel safe and secure.
But the network is critical that in a section of the report looking at ongoing challenges, Staying Put is not mentioned.
"The introduction of a national implementation adviser for care leavers in England was a very welcome appointment and it is encouraging to read examples of good practice highlighted in his first annual report," said Fostering Network director of communications and public affairs Jackie Sanders.
"However, we are very concerned that the report, including the Ambitions section, appears to have completely ignored Staying Put - a policy that has the potential to transform the experience of young people leaving foster care, but is currently benefitting woefully too few of these young people.
"This seems to be in complete contrast with the minister's assertion that the state needs to be as ambitious and aspirational as any parent is for their children, and the statement by Mark Riddell, the national implementation adviser, that ‘in everything we do, or change, or develop, we have to ask ourselves, is that good enough for my child?'"