In an interview with The Times of London, Trump said he wanted nuclear weapons arsenals of the world's two biggest nuclear powers -- the United States and Russia -- to be "reduced very substantially".
"They have sanctions on Russia — let's see if we can make some good deals with Russia. For one thing, I think nuclear weapons should be way down and reduced very substantially, that's part of it," Trump was quoted by the newspaper as saying.
Trump also criticized Russia for its intervention in the Syrian civil war, describing it as "a very bad thing" that had led to a "terrible humanitarian situation," The Times said.
Trump said that he would appoint Jared Kushner, his son-in-law, to broker a Middle East peace deal, urged Britain to veto any new UN Security Council resolution critical of Israel and repeated his criticism of President Obama's handling of the Iran nuclear deal.
He praised Queen Elizabeth and said he was eager to get a trade deal done with the United Kingdom.
"We're gonna work very hard to get it done quickly and done properly. Good for both sides," Trump said. "I will be meeting with [British Prime Minister Theresa May]. She's requesting a meeting and we'll have a meeting right after I get into the White House and it'll be, I think we're gonna get something done very quickly."
Trump said he thought that "Brexit is going to end up being a great thing" and welcomed the fall in the value of the pound for having helped to boost the attractiveness of British products abroad, The Times said.