The president used his speech at the forum to attack climate "prophets of doom" and snubbed their "predictions of the apocalypse" in favour of "optimism" for the future.
In the past, the president has characterized the world's largest single market as a "foe" that has taken advantage of the American economy.
The US President and Greta have been involved in a tit for tat since a year ago.
Although the world, through the Paris climate deal, has committed to keeping temperatures well below 2.0C (3.6F) above pre-industrial times and endeavoured to keep the rise to 1.5C, scientists say we are well off that target.
But European Commission chief Ursula von der Leyen emerged from a "very good conversation with" the president in Davos talking up the prospects of a deal covering trade, technology and energy.
Mnuchin also said that the USA was ready to strike a new trade agreement with the United Kingdom after it leaves the European Union.
"I would be very surprised if I had to implement the tariffs", he said. "I didn't want to go with China and Europe at the same time", he said.
The US and European Union agreed to pursue a trade deal in July 2017 as a tentative truce after Trump had taken office and declared a war on America's yawning trade deficits with the likes of China and Europe.
"The world is on fire", she said.
Trump is scheduled to spend the rest of his two-day visit to Davos in meetings with business executives and other world leaders. "It's a proportionate tax and it's deliberately designed as a temporary tax, so it will fall away once there is an global solution".
Mnuchin emphasised the USA was still involved in the OECD dialogue, but insisted that a digital tax was "discriminatory in nature". I did not... I think that some people are... they put it in a level that is unrealistic to a point you can't live your lives.
France, which considered a similar tax, agreed this week to suspend down payments for this year's digital tax after Washington threatened retaliation with tariffs on French wine. "What happens if he reveals what I think about a certain leader and it's not very positive?" he said, adding that Pompeo testifying would also be a risk.
Trump said Wednesday that he "can live either way" with the Senate's decision about whether to call witnesses at his impeachment trial, but argued that testimony by former national security adviser John Bolton could pose several concerns.
"We're very much looking forward to a new trade agreement with the U.K. That's a big priority of ours for this year".
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