Mr Trump took to Twitter last night, replying to a video of her speech and writing in an apparent sarcastic dig: ""She seems like a very happy young girl looking forward to a bright and wonderful future. So nice to see!"
Mr Varadkar was asked about Mr Trump's intervention at a press conference in New York today.
He said: "I think she's a really passionate person who has inspired young people across the world.
She told the gathered politicians she did not believe they understood the situation, because if they did and continued to fail to act, they would be "evil" and she refused to believe that.
The teenager set out the scale of the challenge in cutting emissions to keep temperature rises to 1.5C, beyond which scientists have warned the impacts of climate change become much more severe - warning that at current rates, the remaining budget for emissions would be used up in eight-and-a-half years.
And she warned that the situation could not be solved by "business as usual" and some technological solutions.
Greta Thunberg at the UN. Photo: Timothy A. Clary/AFP/Getty
"The eyes of all future generations are on you. If you choose to fail us, I say we will never forgive you."
She added: "Right now, right here is where we draw the line. The world is waking up, change is coming, whether you like it or not."
UN secretary-general Antonio Guterres, who convened the summit to urge increased action on tackling emissions, welcomed the young people who have been protesting over climate change.
"My generation has failed in its responsibility to protect our planet. That must change. The climate crisis is caused by us, and the solutions must come from us."
He said the world had the tools, the technology and the imperative, provided by "undeniable and irrefutable" science, and said tackling emissions would deliver other benefits in areas such as health, food security and equality.
Mr Guterres said: "There's a cost to everything but the biggest cost of all is doing nothing, the biggest cost is subsidising a dying fossil fuel industry, building more and more coal plants, and denying what is plain as day: we are in a big climate hole and to get out, we must first stop digging."
Strong message: German Chancellor Angela Merkel talks to climate activist Greta Thunberg during her visit to the UN. Photo: Steffen Seibert/Bundesregierung/Handout via REUTERS
While he said the climate emergency was a race the world was losing, it is a race that could be won, and urged leaders to "lace up our running shoes and win the climate race for us all".
The UN estimates there needs to be between a three-fold and five-fold increase in efforts to cut greenhouse gases, to prevent global temperatures rising more than 1.5C above pre-industrial levels and avoid the worst impacts of climate change.
The climate action summit in New York aimed to galvanise efforts by countries and businesses to close the gap between what is needed to curb global warming and current policies, which put the world on track to warm by more than 3C.