Boris Johnson's ideas for how cash replacing EU aid is spent in Wales post-Brexit are "entirely unacceptable", first minister Mark Drakeford said.
He said Mr Johnson's comments confirm "some of the fears" he had around Conservative plans for a replacement Shared Prosperity Fund.
But Mark Drakeford welcomed the pledge to match what Wales gets from EU funds.
The Tory contest frontrunner made the comments at a hustings in Cardiff.
Foreign Secretary Jeremy Hunt also told the audience at the All Nations Centre that "Wales will not lose out" on funds.
Under EU structural funds Wales would have received more than £5bn by 2020.
But Mr Johnson went further by saying there should be a "strong Conservative influence" over how the replacement money is spent in Wales despite it being currently administered by the Welsh Government in Cardiff.
Asked about the comments at the Welsh Assembly's External Affairs Committee, First Minister Mark Drakeford said it was "good to have confirmation that the money in full will come to us, if that is what that is, because we've never had that confirmed by any UK minister up until now."
"But we have always said, 'not a penny lost, not a power stolen', and while the 'penny lost' may be helped by that statement, the 'power stolen' is certainly not."
He said: "These are powers that have been devolved to the National Assembly for 20 years so Mr Johnson's assertion could only mean a reduction in devolved competence."
"It unfortunately fulfils some of the fears that we have had about some of the thinking that lies behind the 'Shared Prosperity Fund'," he added.
Mr Drakeford said he would not want the UK government to be "judge and jury" in reviewing how the money under a replacement system is spent, but suggested the Welsh Assembly could play an oversight role.
On Sunday, Labour MP Stephen Kinnock urged his party to back Theresa May's withdrawal agreement on Brexit in order to avoid leaving the European Union without a deal.
Mark Drakeford said: "I just don't think that there is a deal, certainly not the deal which Mrs May struck, which can be put in front of the House of Commons and succeed."
The first minister said that is why his government and Welsh Labour has changed policy to fully support a second referendum and the UK remaining in the EU.
During the evidence session, Plaid Cymru AM Delyth Jewell pressed the first minister on whether his support for the Union was "unconditional".
Mr Drakeford said: "If you believe the UK is a voluntary association of four nations you have to face the possibility that some component parts of the United Kingdom may no longer choose to be part of it.
"If that were to be the case in future then of course, any sensible political party or government would have to reassess Wales' place in the components that were there in the future.
"So in that sense it can't possibly be unconditional because there are other moving parts here of which we are not in control."
Ms Jewell said the comments hinted at potential support in the future for Welsh independence.
But a Welsh Government source said Plaid Cymru was "deliberately misrepresenting" the first minister's comments because independence is "for them, the first, second, third, fourth, fifth item on the political agenda".
The source said the Welsh Government would assess what was in Wales' best interests based on UK-wide developments but that that did not amount to support for independence.