The government plans to take a second look at its own proposals for parental flexible working, reports say.
Unions and family organisations say the government should implement its plans for flexible working for parents because there is "massive demand".
This week the government's business secretary Lord Mandelson said proposals would be reassessed.
Business groups have made representations to the government around their concerns about the economic situation.
The government had planned to introduce new rights for working parents next April but this could be delayed.
Parenting groups Mumsnet.com and Dad Info said a survey of more than 3,000 parents showed 70 per cent did not have the right working arrangements for them.
Justine Roberts of Mumsnet said: "Mums and dads are saying loud and clear that they need the option of flexible working to make family life work."
However, a government spokesperson underlined the importance of implementing the right schemes and regulations in light of global business issues.
"It is only right that the government looks afresh at forthcoming regulations in light of the global economic downturn," the spokesperson added.
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