More than 1.4 million young people around the world took part in school strikes for climate action, according to environmental campaigners.

Greta Thunberg, the 16-year-old Swedish student whose solo protest last August prompted the global movement, said: “We proved that it does matter what you do and that no one is too small to make a difference.”

Children walked out of schools on Friday in 2,233 cities and towns in 128 countries, with demonstrations held from Australia to India, the UK and the US, according to the Fridays for the Future website. Further strikes are planned for 12 April.

Eyal Weintraub, an 18-year-old from Argentina who took part in the protests, said: “We have reached a point in history when we have the technical capacities to solve poverty, malnutrition, inequality and of course global warming.

Play Video 1:51 Students around the world go on climate strike – video

“The deciding factors for whether we take advantage of our potential will be our activism and our international unity.”

The strikes inspired by Thunberg drew widespread praise, with UN Women saying on Twitter: “She is proof that we need to listen to the young generation for a sustainable future.”

The executive director of Oxfam International, Winnie Byanyima, said: “Our children are walking out of school saying we have failed them. This is the kind of clarity and energy we need now.”

However, education ministers in the UK and Australia condemned the strikes and some commentators were critical. Madeline Grant, formerly of the Institute of Economic Affairs thinktank, asked: “Just how kind is it to shower praise on children who are fundamentally wrong?”

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Thunberg posted a response on Facebook to “people who wants us to go back to school”. “The favourite argument here in Sweden, and everywhere else, is that it doesn’t matter what we do because we are all too small to make a difference. [But] Friday was the biggest day of global climate action ever, according to 350.org,” she said.

“People keep asking me ‘What is the solution to the climate crisis?’. They expect me to know the answer. That is beyond absurd, as there are no ‘solutions’ within our current systems.

“We need a whole new way of thinking. The political system that you [adults] have created is all about competition. You cheat when you can because all that matters is to win. That must come to an end.

“We need to start cooperating and sharing the remaining resources of this planet in a fair way. We are just passing on the words of the science. Our only demand is that you start listening to it, and then start acting.”

• This article was amended on 20 March 2019. An earlier version referred to the next planned strike date as 15 April. The correct date is Friday 12 April.