Jeremy Corbyn has goaded Nicola Sturgeon into an attack on his leadership of the Labour party after he claimed Scotland could not afford to become independent.

Corbyn told an audience of Scottish Labour MSPs and activists in Glasgow that independence would be a serious mistake, and would lead to “turbocharged austerity and a glaring hole in the money required to fund essential services”.

Referring to Scotland’s £15bn public spending deficit after the collapse in oil prices, Corbyn said on Friday the first minister was surrendering to Tory tax cuts and big business by refusing to raise Scottish income tax rates while cutting council funding.

In an immediate retort on Twitter, Sturgeon said his claims were “rubbish”, adding that “if Corbyn wasn’t leading such a pitifully ineffective opposition, Tories wouldn’t be getting away with half of what they are”.

Nicola Sturgeon (@NicolaSturgeon) Rubbish. And if Corbyn wasn't leading such a pitifully ineffective opposition, Tories wouldn't be getting away with half of what they are https://t.co/1bMOfonMKt

Sturgeon had told MSPs on Thursday the decision on whether to stage a second independence referendum was now “looming” more than ever after Theresa May effectively quashed Sturgeon’s hopes of a special deal to allow Scotland continuing access to the EU single market.

Their spat focuses attention on the reinvigorated battle over Scotland’s constitutional future, with Sturgeon fuelling expectations she is poised to call a fresh referendum on independence before the UK formally quits the European Union in 2019.

Corbyn confirmed on Friday he supported calls from Scottish Labour leader Kezia Dugdale to restructure the UK on federal lines, increasing the decentralisation of power to devolved parliaments and regions, as an alternative to independence.

He endorsed a call from his critic and previous opponent Gordon Brown, the former Labour prime minister, for the UK to return EU powers over farming, fisheries and social programmes to devolved parliaments. Scotland should also have power over VAT sales tax and employment rights after Brexit.

Corbyn added that while Scotland had “the talent and ability to run its own affairs”, it would be financially calamitous, since so much economic power rested outside Scotland. He said its best option was to fight for overall reforms of the UK economy and constitution.

“Brexit provides us with the chance [to] fix a rigged system that doesn’t work for the majority of people. It is pointless to repatriate powers and resources from so-called faceless bureaucrats in Brussels if they are locked away in Downing Street,” he said.

“Labour’s mission in the 20th century was to redistribute wealth and reduce inequality. Our mission in the 21st century must build on that by also redistributing power, wealth and opportunity to every part of our regions and nations.”

Labour hopes this new focus on a centre-left model of federalism, including the replacement of the House of Lords with an elected senate for the nations and regions, would win back hundreds of thousands of voters who have deserted to the SNP or the Tories in Scotland.

Scottish voters are increasingly reluctant to back calls for a snap second independence referendum: only 34% of voters in a BMG poll for the Herald earlier this month backed one in the next year. And overall support for independence now is at about 45% – lower than the 53% peak immediately after the June EU referendum.

There were signs of a split between Dugdale and Corbyn over the scale of that constitutional reform when earlier this month he failed to endorse her calls for a new “Act of Union” – a reference to the 1707 statute which merged the Scottish and English parliaments at Westminster.

Corbyn brushed off a question on whether they were at odds and insisted it was a difference of language. They both agreed that Labour would set up a UK-wide “people’s convention” to investigate constitutional reform. “If you’re looking to report some fight between Kez and me, you better look somewhere else. You won’t find one here this morning,” he said.

Labour officials insist the pair have a close and warm working relationship. But with opinion polls putting support for Scottish Labour as low as 15%, the party is set to lose control of key councils including Glasgow and Fife to the SNP in the local government elections in May.

With Dugdale openly backing Corbyn’s leadership rival Owen Smith last year, Scotland was the only Labour area where Smith outpolled Corbyn. The latter is less popular in Scotland than Tory prime minister Theresa May: only 18% of voters in a YouGov poll for the Times in November thought Corbyn was doing well; 36% of Scottish voters thought May was doing well.

While the UK Labour party is now solvent for the first time in decades after its funds were swollen by a surge in new members, the Scottish party is effectively broke.

The Electoral Commission disclosed on Thursday that Scottish Labour was heavily outspent in last year’s Holyrood elections by the SNP and Conservatives, when it slumped to an embarrassing third place behind the Tories. It spent £338,000 against £1.47m by the SNP and £979,000 by the Tories.