Primary teachers are looking for a new offer from the Government to stave off a potential two-day strike after a successful first strike today.

NZ Educational Institute lead negotiator Liam Rutherford said the union was willing to negotiate when it meets Ministry of Education officials again on Thursday and Friday next week, but it expected the ministry to give some ground.

"It's the job of the ministry to bring an offer that they think is going to be addressing our issues to the table," he said.

"We are going to be hoping that the effect of having 30,000 teachers and parents in support out on the street will have led to some movement."

Today's one-day strike, which the ministry said closed at least 76 per cent of primary and intermediate schools, drew about 7000 teachers and supporters on to Queen St in Auckland and thousands more to protests from Kaitaia to Invercargill.

Institute president Lynda Stuart in Auckland, and other speakers at the other rallies, asked the crowds whether their next step should be rolling regional strikes, or a two-day national strike.

Only a handful chose regional strikes, and the crowds in Auckland, Wellington and Christchurch roared their approval for a two-day strike.

Prime Minister Jacinda Ardern unexpectedly spoke to marchers outside Parliament in Wellington, placing herself on the same side as the teachers.

"There is no you and us," she declared. "There is only us, and if there is only us that means we have to tackle every challenge that you have raised."

But she told Stuff in an interview the teachers had gone on strike too soon, after the Education Ministry's first offer of pay increases of 6.1 per cent over three years for most teachers.

"When you compare where we were with the nurses ... there were four offers in total before they made that decision. In this case there has been one, so I think there were still conversations to be had," she told the agency.

Education Minister Chris Hipkins said the teachers' claim for a 16 per cent pay rise over two years was "significantly higher than anybody else is getting", adding: "There is going to have to be significant movement on their side."

Rutherford said two days of mediation on August 2-3 failed to make any headway.

"The mediator did a good job at keeping the discussion going back and forth, but at the end of mediation there was no new offer on the table," he said.

He said the union's strategy had been led by the members, who wanted to strike because they were frustrated by the ministry's "insulting" first offer.

"It was the teachers of this country that asked to turn a proposed half-day strike into a full-day strike," he said.

Apart from the pay claim, he said the union's approach had been to ask the ministry for action on issues such as funding special needs co-ordinators (Sencos) without specifying how many Senco hours should be funded for each size of school.

"We have been less focused on saying what the actual outcome has to be. We have been floating possible scenarios of what solutions could look like, but the actual answers that the ministry wants to put forward are coming through in the form of offers."

He said the questions at the rallies about a two-day strike were "not a binding vote" and any further strike would need to go to a formal vote by all members.

"My personal sense is that it will be whenever the next offer comes out," he said.

"I imagine that will start the next round of industrial action - or if it does what we need it to, that will settle it."