Women are entitled to take a year off for each child
The extension of maternity leave to up to a year may be sabotaging women's careers, the head of the new equality watchdog has warned.
Nicola Brewer, chief executive of the Equalities and Human Rights Commission, said some employers were thinking twice about offering women jobs or promotion.
She said there may be "unintended consequences" of the focus on mothers rather than shared parental leave.
But small businesses said shared leave would increase "administrative hassle".
Ms Brewer said current laws, introduced from April 2007, had unintentionally made "women a less attractive prospect to employers".
She said her concerns had been reinforced when businessman Sir Alan Sugar said many employers discarded CVs of women of child-bearing age.
Women can take statutory maternity leave for up to 52 weeks, with statutory maternity pay for up to 39 weeks.
If entitled to it, a woman can receive 90% of their average weekly earnings for the first six weeks, then up to £117.18 for the remaining 33 weeks.
The last 13 weeks, if taken, are unpaid.
Conditions must be met, such as the woman having had 26 weeks of continuous employment with the same company before going on leave.
Fathers can take either one or two weeks' paternity leave, receiving either £117.18 or 90% of their average weekly earnings if this is lower.
However, employers can offer their own schemes offering higher levels of pay and longer leave if they want to.
Ms Brewer told BBC Radio 4's Today programme there was a need for "much more genuinely flexible approaches to work", not just for parents, but also for carers, disabled people, and for older people wanting a gradual approach to retirement.
"Within that issue of more flexible working is the specific issue of the unintended consequences of an exclusive focus on maternity rather than parental leave," she said.
"There's an issue about how the whole package of parental leave is currently structured - and there's been a very welcome increase in maternity leave, but we think the focus should be on letting parents decide who takes parental leave after the first six months."
However, Stephen Alambritis from the Federation of Small Businesses called for a pause in changes to maternity leave.
"As a kind of reality check, if you had a small employer employing four people and one of those is on maternity leave then that's a quarter of the workforce out of action.
"Transferring the leave from mum to dad will bring another employer into what is a very complex system. Sometimes it's not the leave itself that we are concerned about or the pay, it's the administrative hassle of the leave."
He said that although it was illegal to discriminate against women of child-bearing age, he had heard anecdotally that a few small businesses would not employ such women.
"But to use this as an argument to level up leave for men is too fast. We would like a pause on all this legislation, especially at what is a very difficult time for employers," he told Today.
Ms Brewer agreed that "one size does not fit all".
Union body the TUC said increasing a father's share of parental leave would bring benefits.
General secretary Brendan Barber said: "The idea that extending family-friendly rights would somehow hurt women's job prospects is a myth commonly peddled by employers who don't want to employ women of child-bearing age or give male staff time off to spend with their children.
"Proposals to increase flexible working rights to parents of older children and allow up to six months of maternity leave to be transferred to fathers will help combat these entrenched views about family-friendly rights and will benefit all parents."