With its ministers having failed to agree to the proposal in the Cabinet meeting, NZ First considered the issue at caucus this week and voted not to support the proposal.
NZ First's chief of staff, Jon Johansson, is said to have communicated to Labour chief of staff Raj Nahna on Wednesday that the proposal should not be brought back to Cabinet.
The reasons for NZ First's reluctance to support were two-fold, the Herald was told by people familiar with the party's position.
It would represent an intervention in contract law in an area where many leases agreed since 2012 include provisions for "emergencies" which appear to cover the disruption.
Since 2012, the most commonly used standard format lease, which originated from the Auckland District Law Society, includes a clause which spells out what happens when tenants have "no access in an emergency".
Known as "clause 27.5", it was developed with the experience of tenants who were unable to access undamaged buildings in the red zone following the Christchurch Earthquake in mind.
The Auckland District Law Society issued a statement on April 7 cautioning that the meaning of the clause had not been tested in court, and which some lawyers interpreted as a warning that the clause may not be the solution some imagined.
However, the Government has acknowledged the clause is leading to negotiations.
NZ First is also believed to have taken the position that intervening in the leasing market could allow large foreign owned companies to game negotiations with building owners, which were largely New Zealanders.
This week Labour has maintained that negotiations within Government were ongoing.
Asked for an update on his plans to address commercial rent concerns, a spokeswoman for Little said "the issue is still under active consideration".
During his speech to the Wellington Chamber of Commerce on Thursday, Finance Minister Grant Robertson said tenants with leases using the standard Auckland District Law Society leases "are in a position" to negotiate with landlords over the impact of Covid-19.
"We've certainly had good feedback from right around the country on where many tenants and landlords have come to an acceptable arrangement," Robertson said.
"But we're aware that that hasn't worked in every single case and, yes, the Government is still considering that matter and we hope to have something to say about that in the very near future."
Labour has not directly responded to questions about whether NZ First was blocking its plans.
On Friday, the Prime Minister's office provided a short statement which simply confirmed parts of Little's earlier statement. Later a spokesman for the Prime Minister's office clarified that it did not comment on ongoing discussions.
Johansson, a former academic and political commentator, refused to discuss the matter, as did NZ First leader Winston Peters.
Some other leases have bespoke provisions addressing the issue in other ways. In other areas tenants and landlords have reported disputes over rent.
The Government has not said how widespread it believes the issue is but a group of industry bodies, including Retail NZ, wrote to the Government in April urging it to intervene.