Prime Minister John Key says secondary school teachers need to return to negotiations with the Ministry of Education.
Members of the Post Primary Teachers' Association (PPTA) held a one-day strike on Wednesday, the first such action in eight years.
About 16,000 teachers refused to work in support of stalled collective agreement negotiations.
In Wellington, several hundred secondary teachers marched along Lambton Quay to Parliament. Several hundred also protested in central Auckland.
The action affected most of the country's 280,000 secondary pupils, though the union exempted schools in earthquake-hit Canterbury from the strike.
Most secondary schools were reduced to minimum staffing levels and many classes were cancelled.
The union wants a 4% pay rise, but teachers say that is not the main point of their claim. It also seeks limits on class sizes and more extended study or research leave for teachers.
The Prime Minister says the Ministry of Education's offer of a 1.5% pay rise on settlement and a further 1% rise the following year is reasonable.
Mr Key says union members should not taken more industrial action and the offer is similar to pay rises won already by nurses and police.
The PPTA already has its members' approval for further industrial action if the parties do not return to talks.