"We believe that this is an offer that we believe is the right one," Robertson told reporters.
Peters told Newshub this morning that the Government possibly could do better with the offer.
"Could we do better? Possibly, but we've got to work our way through it. It's no good fighting with a megaphone and negotiating through the media," he said.
Peters later told reporters he meant there were adjustments that could be made but there was no more money.
"There are adjustments you could make within that money but there is no more money in that context. Conditions could be changed, a whole lot of things in terms of recruitment could be refashioned but we haven't got any more money, not in our first Budget.
Peters told Newstalk ZB's Mike Hosking this morning that nurses needed to be patient.
"We can't fix it all in six months, we've had our first Budget, give us a chance. Next year we'll be able to do more, and the year after that, but we can't fix it up all right now."
Health Minister David Clark said the Government needed to hear from nurses about the best way to split the offer between senior and junior nurses.
"My understanding was that the way that this was split between the nurses was something that was worked through with the nurses' union. The membership is now saying that that's not the best way they think the deal could be cut. We need to hear from them what the best way is that the deal should be cut," he said this morning.
New Zealand Nurses Organisation chief executive Memo Musa said yesterday that strike notices would be issued within the next 48 hours but they were also urgently seeking mediation to resolve the issue.
DHB spokeswoman Helen Mason said they would go into the urgent mediation nurses wanted.
"The current offer on the table is an excellent offer, and it's about much more than base pay rates. DHBs are committed to safer staffing, which includes a commitment to an additional 500 nurses to alleviate staffing concerns."
National leader Simon Bridges said it was a situation entirely of the Government's own making.
"They promised the world. They've spent their money in many other directions ... and now they're struggling with the consequences of that."
While nurses and teachers did deserve pay increases, they should not be too large.
"What would be concerning is if you saw dramatically bigger increases there than you're seeing in the private sector," he told reporters.
The way to increase wages was to grow the economy, not through industrial "unrest".
Bridges called it a "perfect storm" of industrial action.
"We've got the nurses ... we've got the teachers, we've got MBIE. We've got IRD, then we've got bus workers, I think we've got port workers. There are a series of strikes going on here and they are of the Government's making."