Anthony Albanese has all but declared victory over the inflation crisis in an upbeat campaign rally speech promising more free Tafe places and cost of living support.

On Sunday the prime minister addressed a rally in Adelaide, declaring that Australia had navigated through the “global storm” of high prices and has “new reasons for optimism and new proof the worst is behind us”.

The Labor government, which must face an election by May 2025, is slightly behind in the polls as increasing costs including housing and a string of negative stories about Albanese enjoying perks of office including free Qantas flight upgrades weigh on his popularity.

In an attempt to reset the political narrative, Albanese told the rally that the principle of “no one held back and no one left behind” had “guided me my whole life”.

“I’ve never lost sight of that, I’ve never forgotten the people we are here to serve,” he said.

“That’s why my colleagues and I work every day to make a positive difference to people’s lives.”

Albanese said he was “determined to win the next election … to help people through these cost of living pressures, to get more homes built, to get energy prices down, to get more Australians into good jobs, to get Medicare back to its best”.

Looking back at the past term, in which Labor revamped income tax cuts to benefit low and middle income earners and delivered two surpluses, Albanese said “our economic plan has prioritised helping people under pressure while also fighting inflation”.

“When we came to government annual inflation had a six in front of it and was rising.

“Now it has a two in front of it, and it’s falling.

“Our responsible economic management has brought inflation down to its lowest level in almost four years.”

Albanese acknowledged that “the past few years have been difficult”.

“I know workers, families and small businesses have all done it hard,” he said.

“But while there are still challenges to meet, still problems to solve, still people under pressure who need our help, when we look at the economy today, we can see new reasons for optimism and new proof the worst is behind us.

“Together, we have faced a global storm – and we have navigated it the Australian way, the Labor way.

“Not by cutting the services Australians count on, not by denying families the help they need in hard times. But by looking after people – and looking to the future.”

Albanese argued it was still “a time of profound opportunity for Australia” and focused on Labor’s agenda for education, promising “if we act with purpose and urgency, if we invest in our people and trust in their aspirations – we can secure a new wave of jobs and prosperity for every part of our country”.

Albanese said that half a million students had enrolled in fee-free Tafe vocational education and training, accusing the Coalition of framing this policy as “wasteful spending”.

“Today I am proud to announce our government will lock-in free TAFE and make it permanent, nationwide,” he said.

“We will legislate to guarantee 100,000 fee-free TAFE places, each and every year.”

The new places will be created every year from 2027, after earlier commitments to 180,000 places in 2023 and 300,000 places over three years from 2024.

Labor has pledged to cut all student debts by 20% and raise the income threshold for repayments.

Albanese said the debt cut – which will cut the average debt by $5,500 – will be “the first thing we do in our second term” and take effect from 1 June 2025.

Raising the student debt repayment threshold from $54,00 to $67,000 would save someone earning $70,000 about $1,300 a year, he said.

“It helps everyone repaying a student debt right now – and it delivers a better deal for every student in the years ahead.

“Permanent, structural reform to boost take home pay for young Australians.

“This is about putting money back into your pocket – and putting intergenerational equity back into the system.”

Albanese said the policies “are our next big step” in Labor’s agenda to “help Australians earn more and keep more of what they earn”, adding “and they won’t be the last”.

Earlier on Sunday the shadow foreign minister, Simon Birmingham, queried where the money is coming from for the $16bn debt reduction plan.

“This isn’t real reform, this doesn’t change the student fees that somebody who starts next year pays,” he told Sky News.

“This is simply a cash splash … an attempt at trying to con or hoodwink the electorate ahead of the election.”