But the prime minister did not specify how many pensioners would be entitled to claim the payments, when the change would take effect, or how much it would cost the government.
Conservative leader Kemi Badenoch has also said she does not believe "millionaire" pensioners should be able to claim the winter fuel allowance.
But Reform UK, the Liberal Democrats and the Green Party have called for the winter fuel allowance to be restored in full.
More than 10 million pensioners lost out on payments worth up to £300 last year after the Labour government restricted eligibility to those who qualify for pension credit and other income-related benefits.
When asked on Sky News if ministers should be clearer on how they intend to change winter fuel payments, Jones said "it was right that we set out the detail and pay for those things in an orderly way".
He added: "We're sticking to the principle that millionaires shouldn't be getting subsidy for their energy bills from the government, so winter fuel payments will still be targeted to those that need it the most".
He did not provide further details of who would qualify as a millionaire, adding that the eligibility threshold would be reviewed in the "coming months".