A target for a Government scheme aimed at turning around the lives of problem families is "stretching" but will be met, David Cameron has insisted.
The number of families turned around by the initiative almost doubled in the last six months, but ministers were warned there are significant disparities between different parts of the country.
The Prime Minister set out an ambitious plan to help 120,000 "troubled" households by May 2015 as part of his response to rioting in London and other English cities in the summer of 2013.
Blaming the disorder on broken homes, he offered English councils financial incentives to get truanting children back to school, adults into work and anti-behaviour arrested - backed with a budget of more than £400 million.
Public spending watchdogs warned in recent weeks that the initiative risked falling short of expectations, with MPs pointing the finger at a "baffling" failure of Whitehall co-ordination for delays.
The Commons Public Accounts Committee called for further improvements in data-sharing, action to tackle wide variations in the performance of councils and firms delivering the help, and an increase in the pace of progress.
Mr Cameron accepted that the scheme needed to progress "faster" but hailed the latest figures supplied by councils - some of which said they have dealt with three-quarters of the families in their areas - as evidence that people were being assisted and that the taxpayer was saving money.
The Department for Communities and Local Government (DCLG) said the 39,480 families where children had now been to school for three consecutive terms, youth crime and anti-social behaviour significantly reduced and adults found work for at least three months would otherwise have cost the state £3 billion a year.
So far, 111,000 have been identified for help, with 97,000 being actively worked on, DCLG said.
Asked whether the 2015 goal would be met, Mr Cameron said: "It's a stretching deadline but that's deliberate and I think we can meet it, yes.
"What we see from the very best councils, is some of them are more than halfway through turning around these troubled families."
Mr Cameron was speaking after seeing the work of the troubled families team in Wandsworth, south west London.
He said: "Let's remember what this is all about: 120,000 families nationwide with high levels of truancy, of crime, of anti-social behaviour.
"That's bad for them but it's also been costing the country £9 billion. So a third of the way through we have already saved £3 billion; now we need to go faster and get the work done.
"It's a good programme, it's working well and all praise to those who have been taking part in it."
Among councils making good progress are Wakefield in West Yorkshire, which reported that it has helped more than 85% of its targeted families, Leicestershire with 78% and Bristol on 75%.
But Anne Longfield, chief executive of the 4Children charity, warned that success rates across the country were patchy.
"Forty thousand families 'turned around'... is good news. It means 40,000 fewer struggling families falling into crisis, with real rewards for families, communities and the public purse.
"However it also means that there are still 80,000 families who are yet to turn their problems around and there are significant disparities in success between local areas.
"Some areas are not yet joining their services together to provide the intensive support needed. This will be even more important when the programme expands to a further 400,000 families from 2015/16."