Tony Blair says the Child Support Agency is "not properly suited" to its job and is being urgently looked at.
Officials say most compensation payments were for small sums
It was "extremely difficult" to make the CSA - an investigating, adjudicating and enforcement agency all in one - cost effective, he told MPs.
Mr Blair was answering Lib Dem leader Charles Kennedy's criticism of the CSA's "appalling track record".
Mr Kennedy said that for every £1.85 that got through to children, £1 was spent on bureaucratic costs.
The Lib Dems also obtained figures which showed the controversial agency had paid more than 35,000 people compensation for maladministration.
CSA figures show that over the past four years more than 40 claimants have received between £10,000 and £50,000.
The Liberal Democrats have renewed calls for the CSA to be taken over by the Revenue and Customs.
Mr Kennedy said the government's failure to tackle the issue was "disgraceful".
In response, Mr Blair said the CSA had been established by the previous government to make sure parents met obligations to their children.
"The truth is the agency is not properly suited to carry out that task," he said.
The prime minister's official spokesman later said there were "real problems" with the CSA which Mr Blair acknowledged.
"There have been improvements in its performance, but we are not pretending there are not fundamental questions that have to be addressed," he said.
However, ministers have also said the cases in which compensation had to be paid represent only "a tiny percentage" of the cases the agency has to handle.
Government officials insist the vast majority of payouts were for relatively small sums of only around £25.
However, the Liberal Democrats' David Laws said the CSA collected £1.85 for every pound spent on administration, compared to £8 collected under Australia's "far more efficient" system.
"The Inland Revenue is far better placed to track down those parents determined not to pay their obligations," he said.
Action at source
But on Today, Work and Pensions Minister Lord Hunt rejected the Liberal Democrats' call.
"I'm sure the Inland Revenue can help with information and we've been talking to them about that.
"But, at the end of the day, we have to deal with the cases that are currently there and going to come on in."
A Department for Work and Pensions spokesman added that last year the CSA collected "more than £600m" for children.
Following Mr Blair's comments on Wednesday, the Conservatives said Mr Hutton must "clarify the government's intentions as a matter of urgency".
Shadow work and pensions minister Paul Goodman said: "Desperate families have been waiting for government action on the CSA since its last chief executive was forced to resign."
"It's time for clarity - not more spin from Mr Blair."
He said the government must "get a grip on the crisis at the CSA" by cutting bureaucracy and increasing the collection of money.
Since it started in 1993, the CSA has been dogged by controversy. In particular it has suffered computer failures causing severe payment delays.
Last month, it came under fire for failing to answer one-third of telephone calls about its new child maintenance system.