The End Child Poverty Network Cymru (ECPN) welcomed plans for integrated early-years centres in every local education authority and the Assembly's pledge of pound;50 million extra for other early-years initiatives to 2008.
But Lucy Akhtar, the ECPN's co-ordinator, said: "If the Assembly government is to meet its 2020 pledge, it must ensure this strategy is a priority for Welsh local government. Local authorities and other partners should be asked to commit and be given sufficient resources to make it a reality."
A Fair Future for our Children was launched this week by first minister Rhodri Morgan. He said: "Tackling poverty starts with income levels but it goes much wider that that. It is about a child's access to education, leisure, transport and play - it is about engaging them in their future."
The strategy says work is the "best route out of poverty", and ministers have pledged to create 175,000 more jobs by 2010, in the parts of the country where they are most needed.
Other proposals for tackling "income poverty" include half-fare bus travel for 16 to 18-year-olds, to help them get to where the jobs, education and training are, and lessons for schoolchildren on how to manage their money.
But the strategy also highlights the "participation poverty" suffered by some children who miss out on sport, leisure and cultural activities. The Assembly will run a pound;2.5m free swimming scheme during the summer holidays, following a successful pilot last year.
Meanwhile, as TES Cymru went to press, moves to give more powers to children's commissioner Peter Clarke in the fight against child poverty were defeated in the Welsh Assembly.
Plaid Cymru's Rhodri Glyn Thomas said: "The Assembly government has been in power for five years and has done almost nothing to tackle the problem.
"Mr Clarke has described the situation as a national disgrace. I cannot understand why he is not being given extra powers over this area of policy."
Liberal Democrat Peter Black said: "Extending the commissioner's powers will help in a coherent approach to tackling child poverty. We cannot tackle it in isolation."