Kemi Badenoch has been urged by a former Conservative pensions minister to clarify “what on earth she means” by suggesting the pensions triple lock could be means-tested, amid alarm within the party that she will lose support among older people.

The Conservative leader suggested she could back a major policy shift away from the universal promise introduced under her party that the state pension will rise each year by whichever is highest out of 2.5%, inflation, or earnings.

When asked during an LBC phone-in whether she would look at the triple lock, Badenoch said: “We’re going to look at means testing. Means testing is something which we don’t do properly here.”

However, she criticised the Labour government’s move to means-test the winter fuel payment, saying it meant “people who are actually on the breadline actually have had their winter fuel payment taken away”.

Ros Altmann, a non-affiliated peer who previously sat as a Conservative pensions minister, told Sky News on Friday that Badenoch needed to reconsider her comments. “What we urgently need is clarification of what on earth she means,” Altmann said. “What does she mean by means testing the triple lock?”

She added: “The problem we have in going down the route implied – and I don’t think she probably means it – is that every pensioner would start getting a different state pension again. Whereas the whole point of state pension reforms is that there should be a basic flat rate minimum state pension and then encourage people to top it up with private pensions.

“As soon as you introduce means testing to the state pension system, you disincentivise from bothering to save in their private pension.”

Nigel Huddleston, a Conservative co-chair, told broadcasters on Friday that Badenoch had been misinterpreted and said she had indicated she wanted to look at means testing benefits more widely, especially for the wealthy.

But asked by Times Radio whether the UK could afford the triple lock, Huddleston said: “Over the long term these are exactly the things we’re looking at, but the Conservative party has a long and proud history of supporting pensioners, this is the whole point.

“In the speech yesterday as well, Kemi said that we need intergenerational fairness so we need to look at what we can do in terms of policy offerings for young people as well.”

Huddleston said the Tories had not yet made any solid commitments on future policy, and would not make them “on the hoof”.

Labour and the Liberal Democrats seized on Badenoch’s remarks to say it showed the Tories were coming after people’s pensions.

Torsten Bell, the pensions minister, said there was “being bold and there’s being plain bonkers”. “No one who thinks for five minutes can believe means testing the state pension is a good idea – but that is what Kemi Badenoch says she’s up for,” he posted on social media.

A Labour spokesperson said Badenoch had “put pensioners on notice – she’s going to cut your state pension”. They added: “The Labour government has taken tough action to clean up the mess the Tories left our economy in, meaning we can guarantee a £470 cash boost for pensioners in April. The Tories have let the mask slip though and are happy to leave pensioners worse off. Yet again, the Conservatives haven’t listened and they haven’t learned.”

Daisy Cooper, the Liberal Democrats’ Treasury spokesperson, said “bungling Badenoch” had come up with a policy of slashing the state pension. “The Conservatives urgently need to clarify what she meant and how many pensioners would lose out,” she said. “The Liberal Democrats are proud we introduced the triple lock and will fight tooth and nail against Conservative attempts to weaken it.”

The Conservatives claimed Badenoch had said she would protect the triple lock but also look at means testing and accused Labour of promoting “fake news”.

A Conservative spokesperson said: “The Labour party is skewing her words for political gain and lying about what she said. We will look at means testing. But the Conservatives have always protected the triple lock. Ignore the fake news! Read the transcript.”