Speaking on LTV, Kucinskis said a planned overhaul of VID involving rotating or sacking corrupt staff will carry on.
However that looked a questionable claim after a press briefing Tuesday morning in which Petersone revealed the main reason for her resignation was a belief that despite lots of talk and countless policy documents, she felt her effort to actually reform public administration was futile.
"Public administration is not a team with a common goal," Petersone said, "Tensions within the team are enormous."
She hinted that most of the opposition to her reforming efforts came not from within VID but from allied institutions with which it works.
""We have done a lot to help VID become a more modern and a more open institution, but it requires the support of the whole of the public administration. VID alone will not accomplish anything," she said.
Different parts of public administration are pursuing their own goals instead of working together for the good of society at large, she said.
Though she singled out Kucinskis and finance minister Dana Reizniece-Ozola for praise saying their efforts at reform were genuine, their support was not enough to convince her that the reforms could actually be made to stick in an organization determined not to mend its ways.
Speaking earlier in the day Reizniece-Ozola, who initially asked Petersone to reconsider her decision, suggested it was cumulative pressure from a number of sources and was doubtful if Petersone could be persuaded to change her mind.
"From our side we have given her maximum support and it is difficult to say exactly where the pressure on her has come from," Reizniece-Ozola said.
"If Mrs Petersone insists on resigning there is actually no way I can refuse to accept it, but I hope she thinks about it," she added.
"But if Mrs Petersone does hand in a month's notice then in a month's time we will have to find a replacement by means of an open competition," the finance minister explained.
Former finance minister Andris Vilks said on twitter that Petersone had been the victim of pressure exterted from "the political and criminal world" in order to ensure a compliant chief of the tax service.
Politiskais aprēķins un noziedzīgās pasaules spiediens liek atkāpties I.Pētersonei. Gan jau ir padomāts, kas tālāk paklausīgi stūrēs VID.— Andris Vilks (@AndrisVilks) May 30, 2016