The presumptive Republican nominee’s comments came as he arrived at Trump Turnberry in Scotland for the reopening of the refurbished Open venue golf resort.
Donald Trump added his name to the Ayrshire hotel and golf course after buying the resort for an undisclosed fee in 2014.
Comedian Simon Brodkin later disrupted Donald Trump’s news conference by waving golf balls with a swastika on them.
Donald Trump was also the subject of a small protest by those who accuse him of “racism and bigotry” during his bid for the presidency.
Dozens of people, with placards stating “No To Racism”, gathered outside the resort before Donald Trump arrived.
He was asked about the EU referendum result, which saw Leave beat Remain by 52% to 48%, shortly after he touched down at Turnberry in a helicopter.
Donald Trump said: “I think it’s a great thing that’s happened. It’s an amazing vote, very historic.
“People are angry all over the world. They’re angry over borders, they’re angry over people coming into the country and taking over and nobody even knows who they are.
“They’re angry about many, many things in the UK, the US and many other places. This will not be the last.”
Donald Trump said UK divisions “will heal” as “it is a great place”, adding: “I said this was going to happen and I think it is a great thing.
“Basically, they took back their country. That’s a great thing.
“I think we’re doing very well in the United States also, and it is essentially the same thing that is happening in the United States.
“I want to support my son who really represented me here in building this great great place (Turnberry).”
When asked his opinion on UK’s PM David Cameron announcing he is to step down as prime minister after the Leave vote, Donald Trump said: “Well, that’s too bad.”
Speaking later at a news conference, Donald Trump acknowledged his family connection with Scotland through his mother Mary MacLeod, who was born in Stornoway in the Outer Hebrides.
“She loved Scotland, she would be here a lot,” he said.
“She would come every year with my sister Mary and my sister Elizabeth and they just loved it. Her loyalty to Scotland was incredible.”
Donald Trump said his mother would often visit Turnberry for dinner with friends but she never played golf.
He said it was “an honor” to have taken ownership of the resort, which he acquired from Dubai-based Leisurecorp two years ago, before adding his name to the brand.
Donald Trump owns more than a dozen golf resorts in the US and opened his first in the UK, at the Menie estate in Aberdeenshire, in 2012 after controversy surrounding planning, environmental issues and clashes with local people who refused to move.
Turnberry is one of 10 UK golf courses to host the Open golf championship on a rotational basis.
The tournament has been played there on four occasions, most recently in 2009.
The Open is expected to be played in England in 2020 and at St Andrews in 2021, meaning the earliest it could return to Turnberry would be 2022.
Donald Trump’s news conference was interrupted comedian Simon Brodkin, also known as Lee Nelson, who attempted to hand out golf balls with a swastika on them. He was escorted away by security officials.
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