Trump's news conference at his Turnberry golf course in Scotland took place the day after the Brexit referendum -- once the results were already known.
In a Fox News interview before the referendum, Trump recommended UK voters vote to leave Brexit.
On Thursday evening, UK lawmakers voted in favor of delaying the Brexit process and instructed May to ask the EU for an extension, potentially delaying the official exit date until later in the summer.
Trump said it's unlikely the British could take another vote but he would like to see it worked out so the US could do a "very big trade deal" with the UK in the future.
Trump invited his Irish counterpart, the prime minister, a position known in Ireland as taoiseach, to weigh in, and Varadkar noted that he had a "different opinion" from Trump.