“The famous €1bn is guaranteed by no foundation, no authority,” he said in a statement.
The archbishop stressed that he was not calling any pledges into question but said “the fact remains that most of these donations have not yet been made.”
His statement was a response to claims from a French heritage foundation, which has halted fundraising for the cathedral as it says enough money has been gathered.
The Gothic cathedral which stands at the heart of Paris, was severely damaged in a fire on 15 April 2019.
Last week the Fondation de Patrimoine, a state backed heritage group, announced that it would no longer be collecting funds for the damaged cathedral.
The foundation was one of four organisations tasked with officially collecting money for Notre Dame.
Guillaume Poitrinal, its chair, said the group had raised nearly €900m (£790m) and urged people to donate to other churches.
“We’ve got a full tank,” he said.
But Archbishop Aupetit disputed the account and pointed out that the cost of the restoration was still unclear.
“The necessary budget...is still unknown,” he said.
He added that €9.5m had been raised from 43,000 individual donations given by French and foreign nationals, in particular US citizens.
A further four million has been given by major donors.
“The collection continues,” the archbishop said. “The needs appear considerable.”
Mr Poitrinal told the Liberation newspaper that he believed that the high profile figures who had pledged to donate would honour their promises.
“I cannot believe that [they] would withdraw,” he said.
But Franck Riester, France’s culture minister, urged caution earlier this week.
“It is premature to think that we have too much money collected,” he said.
Additional reporting by agencies
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