Labour has urged the new work and pensions secretary, Stephen Crabb, to appear before parliament on Monday to announce formally that controversial cuts to disability benefits that triggered the resignation of Iain Duncan Smith will be dropped.

Owen Smith, the shadow work and pensions secretary, welcomed Crabb’s appointment, and said: “His very first act as secretary of state must be to come to parliament on Monday to announce the full reversal of cruel Tory cuts that will see 370,000 disabled people lose £3,500 a year.”

He also urged Crabb to “learn to stand up to a Treasury that – on George Osborne’s watch – is intent on cutting support for those most in need to pay for tax breaks for those who least need them”.

Labour is keen to exploit the disarray in government to see off the disability cuts – which government sources have signalled will be kicked into the long grass – and ramp up pressure on the chancellor. The savings to personal independence payments (PIP) for the disabled were slated to bring in more than £4bn over the course of the parliament, helping Osborne to meet his target of delivering a surplus on the public finances by 2020.

Crabb indicated on Saturday that the cuts would not go ahead. He told a local radio reporter in Pembrokeshire, where he is the local MP: “We are not going to be going ahead with these cuts to the disability benefits that were proposed on budget day, the prime minister has confirmed that himself, and I was very clear when I discussed the offer of a job with the prime minister this morning, that we were not going to go ahead with he cuts that were being proposed.”

The Labour leader, Jeremy Corbyn, called for the chancellor to step down after Duncan Smith’s resignation, blaming him, as the architect of austerity, for the disability cuts that had prompted a rebellion on Conservative back benches.

On Saturday, Corbyn said he would be “back on his case in parliament next week” over planned spending cuts.

In an interview with Sky News, he welcomed Duncan Smith’s resignation and added: “I wonder where his conscience has been hiding for the past six years.

“I think he has done the right thing to resign, because after all this is a man who has presided over some fairly appalling policies but this latest example of cutting the personal independence payments of a very large number of people ... is shocking,” he added.

“He has resigned, but I really think the problem is the chancellor of the exchequer, George Osborne.”

In a sign of growing public opposition to cuts to disability benefits, 150,000 people signed a petition organised by the campaign group 38 Degrees in the 24 hours after it was set up, calling for PIP cuts to be cancelled. Adam McNicholas, media campaigns manager at 38 Degrees, said prolonging uncertainty over cuts was “cruel and unjust”.

Friends of Duncan Smith said he quit because of the refusal of Downing Street and the Treasury to consider cuts to universal pensioner benefits, rather than benefits for working-age people and those with disabilities.

Allies of Corbyn see the departure of the Duncan Smith as a vindication of their anti-austerity stance: Duncan Smith used his resignation letter to the prime minister to suggest the cuts to PIP were “not defensible in the way they were placed within a budget that benefits higher-earning taxpayers”.

They believe Corbyn’s argument that the budget had “unfairness at its very core”, when he responded in the House of Commons last Wednesday, struck home with Conservatives, and contributed to Duncan Smith’s discomfort.

Richard Burgon, a Labour backbencher and Corbyn loyalist, said: “Jeremy Corbyn was elected leader and John McDonnell was appointed as shadow chancellor on the basis of their key analysis that austerity is a political choice, not an economic necessity. Events are proving them right.”

Diane Abbott, a close ally of Corbyn, tweeted that Duncan Smith was the Labour leader’s first “scalp”.

Ian Duncan Smith. First big scalp of the Corbyn era #corbyn4pm pic.twitter.com/pOnPROlvW9 — Diane Abbott MP (@HackneyAbbott) March 18, 2016

With rival groups within Labour starting to organise themselves to promulgate alternative policies to those espoused by the leadership – and speculation mounting of a potential leadership bid after the June referendum – Corbyn’s allies believe his position has been shored up by the Tories’ disarray.

Duncan Smith suggested in his resignation letter that the latest planned cuts in public spending were increasingly being seen as driven by political, rather than economic, considerations – an argument long made by Corbyn and his supporters.