"We young people are waking up and we promise, we won't let you get away with it anymore," 16-year-old Thunberg told delegates. She was speaking after green parties emerged as one of the big winners in the European parliamentary elections.
Climate change was "the biggest crisis that humanity has ever faced," said Thunberg. "It is not something you can 'like' on Facebook."
Technological developments in fields such as electric cars and solar energy should not leave people with the impression that they could "solve the crisis without making any efforts", she said.
"Once we realize, we act, we change. Humans are very adaptable," she added.
Thunberg has become a figurehead for young climate activists internationally, inspiring hundreds of thousands of other youths to strike from school in "Fridays For Future" protests.
She was speaking at the Austrian World Summit, an initiative launched by Schwarzenegger, which brings together some 1,200 figures from the worlds of science, politics and business to discuss ways to tackle climate change.
Greta Thunberg, centre, with Alexander Van der Bellen and Arnold Schwarzenegger at the opening of the summit. Photo: Georg Hochmuth/APA/AFP
In a speech at the event, Schwarzenegger called on world leaders to "stop lying to the people about pollution and about the climate change" and to "invest in the green energy of the future".
UN Secretary General Antonio Guterres regretted that "many of the countries that in Paris promised to do a number of things are not even catching up with their own promises".
The 2015 Paris agreement, negotiated under the auspices of the UN, enjoins nations to cap global warming at "well below" two degrees Celsius (3.6 Fahrenheit). But US President Donald Trump pulled out of the accord in 2017.
"Climate disruption is upon us, and it is progressing faster than our efforts to address it," Guterres said.
In Sunday's European parliament elections green parties managed double-digit scores in some of Europe's biggest countries, including 20 percent in Germany.
Polling data indicates younger voters in particular turned towards environmentalist parties in order to put climate action more firmly on the agenda.