New Zealand Government Procurement general manager Laurence Pidcock said the tender, which opened on August 5 and was due to close on September 30, had received "an incredible amount of interest".
He said MBIE engaged with stakeholders before the tender opened, but clearly not all voices were heard.
The current contract, in place since 2017, involves 41 recruitment firms doing work for 179 government agencies. It was worth $142 million in the last financial year.
Under the proposal, recruiters must charge the same for filling low-skilled and low-paid roles as they would for filling more skilled and better-paid jobs.
Recruiters would set different fees for permanent/fixed-term roles and contractors from temporary roles.
They would also set different fees for two broad job classes the contract relates to – "common administration and corporate" and common IT.
The former category includes roles in accounting and finance, admin, asset management, health and safety, general management, policy, procurement, and project management.
The "common IT" category includes roles in cyber security, network engineering, IT support, and web development among others.
Pidcock acknowledged a move to fixed fees would be a "significant" change from the status quo.
He said the aim was to provide the best value for taxpayers while also ensuring Government agencies got transparency and value for money from recruiters.
But recruiters believed the fixed fee model was unsustainable and would put firms' public sector clients out of step with their private sector ones.
RCSA chief executive Charles Cameron said: "Right now, New Zealand is experiencing the greatest talent crisis in its history and Government is a lead driver of demand.
"It has never been more important to ensure that Government's settings for acquiring talent make them an attractive client for staffing firms in a highly competitive market."
There is currently no shortage of government work for recruiters, with an additional 3,423 full-time staff and contractors needed to fulfil commitments made in this year's Budget.
Finding staff is difficult across the board, due to the tight labour market. But pressures are expected to abate as economic growth remains sluggish and immigration picks up.
MBIE expects the tender process will continue after the four-week pause, but it said it would provide an update on September 30.
The new contract is due to take effect in September 2023. It will have a term of three years, with two rights of renewal of three years each.
The only part of the proposed new contract back on the table for discussion is the pricing model.