Rishi Sunak has been urged to keep the £20 increase in a letter signed by Amber Rudd, Esther McVey, Damian Green, Stephen Crabb, Sir Iain Duncan Smith and David Gauke.
The former welfare secretaries warned the uplift was "vital for protecting the incomes of many families and providing support to the economy".
They wrote: "As former secretaries of state for work and pensions, we are writing with one voice to support those individuals and families that are struggling most in the wake of the pandemic, and to ask that the current funding envelope for individuals on universal credit be kept at the current level.
"Work remains the best way out of poverty for those who can work, but we want to make sure that those who cannot work are supported with dignity."
Mr Duncan Smith added that the benefit system was "one of the greatest, but unremarked, successes of the government's response to Covid".
He continued: "The extra £20 has been essential in allowing people to live with dignity.
"This investment should be at the heart of what makes us Conservatives: delivering the policies needed to provide businesses and people across the UK with opportunities to prosper, whilst simultaneously providing support to those at risk of being left behind."
Mr Sunak announced earlier this year that the £20-a-week increase would remain in place until the end of September.
The cabinet is believed to be divided on making the increase permanent, with Mr Sunak at odds with the work and pensions secretary Thérèse Coffey.
Treasury estimates show that the £20-a-week uplift costs about £6 billion a year.It comes as the SNP Westminster leader Ian Blackford warned there was a "very real danger" planned cuts to furlough, Universal Credit and business support by the autumn could push millions of people into poverty and cause widespread unemployment.
He added: "Millions of families are already living on the breadline and struggling to get by.
"The £1,040 cut to Universal Credit must be reversed altogether with a complete U-turn, otherwise we will inevitably see a Tory poverty crisis this winter.”