And as he begins to set out what his presidency will be like, he has distanced himself from far right groups which supported his campaign.
The possible change of heart over climate change was revealed during an interview with editors and reporters at the New York Times.
He said he would “keep an open mind” about the Paris accord on limiting carbon emissions, which he had previously said he would re-negotiate or even scrap.
In 2014 he tweeted that “Global warming is an expensive hoax!”, and he said it was created by the Chinese to make US manufacturing less competitive.
But now he says: “I think there is some connectivity. Some, something. It depends on how much.”
It comes in the wake of another change of heart, the news that he will not be pressing for Hillary Clinton to be prosecuted over her use of a private email account.
Mr Trump used his talks at the New York Times to attack alt-right groups which have supported his campaign.
Pictures have emerged of white nationalists giving Nazi salutes as they celebrated his election victory.
“I condemn them. I disavow, and I condemn,” he is reported to have said, adding that he did not want to energise groups linked to white nationalist, anti-Semitic and racist ideologies.
“It’s not a group I want to energise,” he said. “And if they are energised, I want to look into it and find out why.”
One campaign promise Mr Trump does seem determined to follow through on is his intention to walk away from the Trans-Pacific Partnership (TPP).
German Chancellor Angela Merkel is the latest world leader to be unhappy about Mr Trump’s announcement.
“I will tell you honestly, I am not happy that the trans-Pacific agreement now will probably not become reality,” she said.
“I don’t know who will benefit from that – I want to hold back with forecasts.
“I know only one thing, there will be other trade agreements, and they won’t have the standards that this agreement and the hoped-for TTP agreement have.
“This has to do with jobs under globalisation, with fair competitive conditions, with shaping globalisation in a humane way. “
The agreement was designed to bring down tariffs and trade barriers between America and a number of Pacific Rim nations including Australia, New Zealand, Japan, Malaysia and Chile.
But Mr Trump described it as a “potential disaster for our country”, and says he will take executive action on his first day in charge to withdraw from it.
Instead he wants to draw up bilateral trade deals with individual countries.
Meanwhile, Mr Trump has announced he has asked Republican rival Ben Carson to head the Department of Housing and Urban Development.
Mr Carson is expected to respond after the Thanksgiving holiday, but has previously said he did not want to be involved in Mr Trump’s administration.
There are also reports in the US media that South Carolina Governor Nikki Haley is being lined up to be the US ambassador to the United Nations.
If it is confirmed, it will be Mr Trump’s first female appointment.