The tribunal ruled against Tvarozkova last month, saying she was liable for $20,000 in unpaid rent and damaged property at a rental property in Wellington.
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"In this case, the Ministry was not notified by any of the parties prior to the Tribunal's hearing," the spokesman said.
"Once notified, in accordance with our legal obligations, the Ministry advised the Tribunal to consider the issue of immunity because at the time of the Tribunal hearing, it was unaware that diplomatic immunity was an issue.
"Once alerted to this fact, the Tribunal ordered a formal hearing to consider the effect of the diplomatic immunity on the case."
A hearing has been scheduled for next month.
The MFAT spokesman said New Zealand could not waive diplomatic immunity for another country.
"This is a decision for the European Union."
A spokeswoman for the EU delegation confirmed MFAT's request, but said it could not comment on whether it was being considered.
The Herald visited Tvarozkova's new apartment today but she refused to answer questions, saying, "we won't be commenting on this".
One of the landlords of the Karaka Bay property, Matthew Ryan, was angry at the way the case had unravelled and was concerned that he would not get his money back.
"I just don't feel like it's cricket. For them to step in and for her to hide behind some sort of immunity."
Ryan said he had expected a high-ranking diplomat to be a reliable tenant.
"I thought I had the security of a three-year tenure but they left [after eight months] with rent arrears, they caused some damage to the property before they left, gave me no notice of leaving.
"And so effectively I was left high and dry. I thought the Tenancy Act would at least allow me to recover the rental shortfall and the damage.
"And so it's pretty disappointing to hear that when you lease to a diplomat you effectively have none of the provisions that you would normally have if [it were] a normal member of the community."