The system "is ready for January 2019", Damarnin's ministry announced on Sunday after a report in Le Parisien newspaper raised serious doubts about whether that would really be the case.
There have been thousands of glitches in tests run by the government and employers over the last year, the paper reported, with as many as 352,000 in February.
It quoted a leaked account of a "crisis meeting" at the economy ministry at which "the civil servants feared the worst" if PAYE is introduced on schedule at the beginning of next year.
The change, which was first mooted under previous president François Hollande, has already been postponed once but was one of President Emmanuel Macron's campaign commitments.
But Le Parisien reported "massive and completely random mistakes", some of which were also recurrent.
The chief culprits were not the ministry, which has recruited an extra 500 employees to prepare for the transition, but employers, in both the private and public sectors.
The txman rings twice
They sometimes sent in lists of employees twice, leading to people paying twice, and sometimes confused surnames, leading to one person paying another's tax.
And if the errors had been reduced to zero by June, they started to reappear in July and August, according to Le Parisien.
Both Macron and Prime Minister Edouard Philippe had already hinted that the transition might not be ready on time before the latest revelations and Darmanin had also shown signs of hesitation.
But overnight he insisted that it was all systems go.
"The test phase for #DeductionAtSource has made it possible to identify errors and correct them (that's its role!)," he tweeted. "The errors identified affected less than 1% of taxpayers, they have been resolved since. The technical mechanism works, it's ready!"
PAYE ready to go, Minister Darmanin tweets
Poke @le_Parisien! La phase de tests du #PrélèvementALaSource a permis d’identifier des erreurs et de les corriger (c’est son rôle!). Les erreurs identifiées concernent moins de 1% des contribuables, elles ont été depuis résolues. Le dispositif technique fonctionne, il est prêt !Gérald DARMANIN (@GDarmanin) 1 septembre 2018
Public accounts boss Bruno Parent also insisted that the change will go ahead as planned, pointing out that "10s of millions" of employees' details were involved in the test.
"There never was a crisis meeting," he told Le Parisien. "There's no crisis whatsoever."
Some government members were more cautious than Darmanin on Sunday.
The minister is to meet Macron on Tuesday.
An opinion poll conducted on Friday and Saturday showed 40 percent of respondents in favour of the change.