A spokeswoman for the Department for Business Enterprise and Regulatory Reform said: "It is only right that in the current economic climate we look afresh at the costs and terms of the new regulations with the caveat of regulatory burden."
She also said that a date for introducing the new leave rules has not been confirmed.
The CIPD voiced worries that sharing parental leave would create unnecessary administrative burdens since, in the majority of cases, parents work for different employers.
Mike Emmott, the CIPD's employee relations adviser, commented: "What would have been cumbersome in good times could become the straw that breaks the camel's back in a recession ? and could damage the long-term business case for better work-life balance."
Mr Emmott argued that the case for more generous paternity leave in the medium term remains a strong one. With workplace demographics changing and with a greater proportion of women now in employment, some improvement in paternity leave is necessary to tackle the problem of the gender pay gap, he added.
But Mr Emmott concluded: "The recession-inspired shelving of the existing proposals must be used by politicians and business leaders to come up with workable proposals that balance competing demands in a way that works for business.