Radiographers say they will cancel a proposed nationwide strike if district health boards can settle their outstanding issues over terms and conditions.
But district health boards say the radiographers' union is trying to renegotiate issues which had already been resolved.
The medical radiation technologists' union APEX has agreed to a pay offer of 1% now and a further 1% in October.
But it wants that backdated to the end of the last collective agreement almost a year ago.
Radiographers also want time in lieu for professional development they undertake in their own time and pay parity for sonographers.
They say all strike action, including a nationwide strike planned for 7 September, will be cancelled if the district health boards agree to their counter offer.
Radiographers at Counties Manukau District Health Board are in the middle of a four-day strike and low-level industrial action is being taken elsewhere.
DHB spokesperson Phil Cammish says the union's offer is nothing new.
He says DHBs are always ready to negotiate but not under the duress of industrial action.