WELLINGTON (REUTERS) - Tens of thousands of students gathered for marches across New Zealand on Friday (Sept 27) to kick off a planned second global school strike for climate action.

The latest round of protests, which builds on last week's marches by millions of children around the world, is planned to roll through Asia and Europe before culminating in a rally in Montreal, Canada, where teenage activist Greta Thunberg is scheduled to speak.

Greta, who is credited with inspiring the school strikes, this week lambasted world leaders for a lack of climate change policies at the United Nations Climate Action summit in New York this week.

In New Zealand, scores of protests were held in towns and cities across the country with students carrying signs including: "We're skipping our lessons, so we can teach you one" and "You can't comb over climate change".

School Strike for Climate NZ, the organiser, tweeted that it had received credible reports that 170,000 people were striking nationwide, a figure that would represent 3.5 per cent of the country's population.

Local media put the crowd in the capital of Wellington, where students were delivering a petition to the national parliament calling on the government to declare a climate emergency, at around 40,000.

New Zealand Prime Minister Jacinda Ardern, who is in New York at the climate summit, on Thursday announced that she had support from four other countries for a proposed new trade agreement to combat climate change.

Ms Ardern said negotiations would begin with Norway, Iceland, Costa Rica and Fiji early next year, adding that she hoped other nations would sign on.

New Zealand protesters were again ready to counter arguments that they should be in school, instead of out on the streets protesting.

"My education doesn't matter if I have no future or if I have no land," Elizabeth Glassie, a protester in Auckland, told Radio New Zealand.

About 500 students in the South Korean capital, Seoul, urged more government action to address climate change, marching towards the presidential Blue House after a downtown rally, where they said the government gets an "F" in climate action.

"I believe government action will change only if the voice of young people are heard because we're the ones...who are going to be the greatest victims of a climate crisis," said 15-year-old Kim Do-hyeon, one of the organisers.