Universal Credit claimants have received an extra £20-a-week boost since April this year in response to the coronavirus pandemic.
However, the Chancellor said the boost was “temporary” and that any decision on its future would come next year.
It also comes as Mr Sunak struggled to defend his cut to overseas aid cut which was unveiled in his Spending Review.
Asked on BBC Breakfast to give people clarification on whether the Universal Credit boost will be extended, he replied: “We put, at the beginning of this crisis, lots of different measures in to help people.
“One of those was a temporary one-year uplift in Universal Credit given that we were dealing with many months of a national lockdown – very severe set of restrictions that that was and a period of acute panic.
“That was a temporary increase, it runs all the way through to next spring and it wouldn’t be right to make a permanent decision about that now when the economic outlook is so uncertain.”
He added: “Let’s get to that point, let’s see where we are with the economy, the health restrictions and then decide what the best way to support people who need our help is and we can make a clearer decision about that next year.”
However, charities have warned that millions of families on Universal Credit are facing “agonising uncertainty” and called on the Government to extend the boost or even make it permanent.
Rashford, who has forced the government into U-turns over free school meals, warned against stopping the extra payments, adding: “Children cannot be living to deadlines.”
He tweeted: “I’m really concerned that families are constantly counting down the days until help is taken away from them.
“The need for long-term change is massive. Children cannot be living to deadlines. We have to stabilise these households. 2.5 million will be unemployed in spring.”
Mr Sunak was also grilled over his cut to overseas aid from 0.7 per cent of national income to 0.5 per cent.
Junior minister Baroness Sugg quit over the move, calling it “fundamentally wrong” at a time of “unprecedented” global crisis. Meanwhile former Prime Minister David Cameron branded it a “very sad moment” for Britain.
Mr Sunak said it was a “difficult decision” but insisted Britain was not turning its back on the world’s poorest
He told Sky News: “Is it a difficult decision? Of course it is a difficult decision - no one wants to be having to make these difficult decisions.
“But this is about an economic emergency that I described yesterday and we’re going to have record-level peacetime borrowing and debt.”