The policy means most families cannot claim means-tested benefits for more than their first two children born after April 2017.
Ms Phillipson’s comments are the strongest a minister has made about the policy potentially being scrapped.
Analysis by The Resolution Foundation thinktank over the weekend found 470,000 children would be lifted out of poverty if parents could claim benefits for more than two children.
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However, Ms Phillipson said the government inherited a “really difficult situation” with public finances from the Conservative government.
“These are not easy or straightforward choices in terms of how we stack it up, but we know the damage child poverty causes,” she added.
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Why did Labour delay their child poverty strategy?
The education secretary, who is also head of the government’s child poverty taskforce, said ministers are trying to help in other ways, such as expanding funded childcare hours and opening free breakfast clubs.
She said it is “the moral purpose of Labour governments to ensure that everyone, no matter their background, can get on in life”.
Her “personal mission” is to tackle child poverty, she said.
Sir Keir Starmer is said to have privately backed abolishing the two-child limit and requested the Treasury find the £3.5bn to do so, The Observer reported on Sunday.
The government’s child poverty strategy, which the taskforce is working on, has been delayed from its original publication date in the spring.
Whether to scrap the two-child benefit cap is one of the main issues it is looking at.