Greta said: “We are in the beginning of a mass extinction and yet all you can talk about is money. You are failing us.”
In a tweet, Mr Trump said: “She seems like a very happy young girl looking forward to a bright and wonderful future. So nice to see!”
But Greta has responded by changing her Twitter bio to "a very happy young girl looking forward to a bright and wonderful future."
Mr Trump had spent only a few minutes at the climate summit, a centrepiece of this year’s UN general assembly schedule.
Greta told delegates on Monday they would never be forgiven by future generations if they failed to tackle rising temperatures in an emotional speech.
“This is all wrong. I shouldn’t be up here. I should be back in school on the other side of the ocean,” she said.
“You have stolen my dreams and my childhood with your empty words, yet I’m one of the lucky ones.
“People are suffering. People are dying, entire ecosystems are collapsing.
“Yet, you all come to us young people for hope. How dare you?"
As Ms Thunberg continued, tears welled in her eyes.