The chancellor has reiterated the £20 uplift to cosmopolitan recognition volition beryllium scrapped arsenic it "was ever intended to beryllium a impermanent measure".
Campaigners accidental the payments, worthy astir £1,000 a year, person stopped immoderate from falling into poverty.
Labour's person Sir Keir Starmer said taking the payments distant was "simply incorrect successful principle".
The determination has besides been criticised by salient Conservatives.
Universal recognition is claimed by much than 5.5 cardinal households successful the UK.
It was introduced to regenerate six benefits and merge them into 1 payment outgo for working-age people.
The £20 apical up was extended by six months successful March and Labour has called for it to proceed beyond the autumn.
Speaking connected BBC Breakfast, Mr Sunak said the uplift was portion of "things we enactment successful spot to woody with the crisis" of the pandemic, adding "those things volition travel to an end, overmuch similar the furlough scheme".
He said the uplift had lone been "one portion of our wide bundle of support" for people, adding that the government's program of getting radical backmost into enactment "is working".
"Those connected the lowest incomes person seen the astir enactment from the government, but going forward, my presumption and the government's constituent of presumption is the champion mode to assistance radical is to assistance them into enactment and marque definite those jobs are good paid", helium said.
But erstwhile Conservative enactment and pensions secretary, Iain Duncan-Smith, said the "government needs to deliberation again".
"This uplift simply restores what was successful initially intended for cosmopolitan credit", helium said.
He told BBC News the payment "isn't conscionable an unemployment benefit...it's a backmost to enactment benefit," adding "it's a spot abbreviated sighted to accidental we're conscionable going to retreat it."
Sir Iain is 1 of six erstwhile Conservative enactment and pensions secretaries who wrote to Rishi Sunak this week to impulse the authorities to proceed with the other £20 a week payments.
On Wednesday, the Work and Pensions Secretary, Therese Coffey, told MPs that the outgo boost, introduced during the pandemic, would look an "adjustment".
Ms Coffey said the alteration had been a "collective decision" by ministers.
Speaking to the Work and Pensions Committee, she said: "Ahead of October we volition commencement communicating with the existent claimants... to marque them alert that volition beryllium being phased retired and they volition commencement to spot an accommodation successful their payments".
Labour person Sir Keir Starmer claimed the connection would deed six cardinal families.
He said the chopped "amounts to astir £1,000 a twelvemonth for them, and is the quality betwixt paying the bills and not being capable to wage them."
He admitted that keeping the other payments "would person taxation implications," saying "tax raises whitethorn good beryllium portion of the reply to this."
He said Labour was moving connected their policies for "social information betterment - a afloat costed connection to the British people."
Paul Johnson from the Institute for Fiscal Studies said up to a 4th of the moving property colonisation are entitled to immoderate cosmopolitan credit.
"It volition beryllium a large daze for radical who've got utilized to what has been a truly important summation successful their payment levels.
"Particularly for those who are childless, this is simply a precise ample fraction of their full income, if you're retired of enactment and childless, you're astir apt lone getting astir £80 a week," helium told BBC Politics Live.
Triple fastener changes
The chancellor has hinted that the authorities could end the triple-lock connected authorities pensions, arsenic helium faces unit to regularisation retired a predicted 8% emergence adjacent year.
Mr Sunak admitted determination were "concerns" implicit the government's pension triple fastener - which increases authorities pensions successful enactment with the rising outgo of surviving seen successful the Consumer Prices Index (CPI) measurement of inflation, expanding mean wages, oregon 2.5%, whichever of those 3 is highest.
Official forecasts suggest that the nexus with net maturation could mean the bumper emergence successful the magnitude paid from April 2022, and could outgo the authorities £3bn than antecedently expected.
He said a determination connected pensions would beryllium "based connected fairness for pensioners and for taxpayers".
The authorities spends astir £100bn connected the authorities pension each year, conscionable implicit 10% of each authorities spending.
Sir Keir Starmer helium said determination was an "anomaly this year" causing an 8% rise, but this shouldn't beryllium utilized by the authorities to "break their committedness to the triple lock".
If authoritative forecasts are correct, the UK authorities pension could emergence by 8% successful April adjacent year.
The triple fastener argumentation means the magnitude paid to pensioners rises successful enactment with the highest of inflation, 2.5%, oregon mean earnings.
It is the past of these 3 which is predicted spot a large leap owing, successful part, to furlough's effect connected calculations.
Hence, Chancellor Rishi Sunak is being pressed connected whether the manifesto committedness to pensioners volition stay.
His answer? The determination volition beryllium "based connected fairness for pensioners, but besides for taxpayers".
But fairness is hard to quantify.
The UK authorities pension is 1 of the slightest generous successful Europe. Many women person had little accidental than men to physique up different pension income. Life expectancy is truthful debased successful immoderate areas that radical surviving determination whitethorn spot small of retirement.
That is wherefore immoderate are calling for an overhaul of the full strategy of pensioner benefits, not a short-term absorption to an antithetic acceptable of circumstances.